Springer proceedings in mathematics & statistics, 2015
This chapter deals with large-scale nonlinear delay stochastic systems where the system states ar... more This chapter deals with large-scale nonlinear delay stochastic systems where the system states are subject to impulsive effects and perturbed by some disturbance input having bounded energy. The interest is to develop a comparison principle and establish input-to-state stability (ISS) in the mean square (m.s.) using vector Lyapunov function and Razumikhin technique. Impulses are being viewed as perturbation to stable systems, and they have a stabilizing role to unstable systems.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
This paper investigates exponential stability of singularly perturbed switched systems with time ... more This paper investigates exponential stability of singularly perturbed switched systems with time delay. The multiple Lyapunov functions technique and dwell time approach are used to establish stability criteria for a switched system consisting of both stable and unstable subsystems. Examples are presented to illustrate the criteria.
This paper addresses stochastic hybrid systems, particularly switched and impulsive systems. The ... more This paper addresses stochastic hybrid systems, particularly switched and impulsive systems. The systems under consideration are linear and non-linear continuous with/without time delay, and with/without external force. The importance of using such systems and the discrepancies between hybrid and non-hybrid systems are presented. The objective of this paper is to survey recent developments on some of the important qualitative properties such as stability, stabilisation, input-to-state stability and state estimation along with the challenges that might arise when taking hybridness into account. These properties are mainly developed by using the direct method of Lyapunov or Lyapunov–Razumikhin if time delay is taken into account. Several examples with simulations are presented to further clarify the results introduced in this paper.
ABSTRACT This paper studies time-delayed switched systems that include both stable and unstable m... more ABSTRACT This paper studies time-delayed switched systems that include both stable and unstable modes. By using multiple Lyapunov-functions technique and a dwell-time approach, several criteria on exponential stability for both linear and nonlinear systems are established. It is shown that by suitably controlling the switching between the stable and unstable modes, exponential stabilization of the switched system can be achieved. Some examples and numerical simulations are provided to illustrate our results.
Springer proceedings in mathematics & statistics, 2018
This paper addresses the exponential stability problem for discrete impulsive switched singular s... more This paper addresses the exponential stability problem for discrete impulsive switched singular systems with time delay where the impulsive effects occur as a result of switching among the subsystems. Some sufficient conditions on the exponential stability of the system are established. The stability conditions are investigated by using the multiple Lyapunov functions along with the average dwell time switching signal and by resorting the Halanay lemma. Finally, numerical examples with simulations are provided.
This chapter deals with the problem of designing a robust reliable decentralized control for impu... more This chapter deals with the problem of designing a robust reliable decentralized control for impulsive large-scale systems (ILSS) with admissible uncertainties in the system states. Then, the same idea is carried over to design reliable observers to estimate the states of the above systems. The faulty actuator/sensor outputs are assumed to be zero. The reliability analysis is achieved by using a scalar Lyapunov function.
In this chapter, we address stochastic impulsive systems with time delay, where the impulse times... more In this chapter, we address stochastic impulsive systems with time delay, where the impulse times are state-dependent. Using Ito calculus, we develop the essential foundation of the theory of the mentioned system, namely local and global existence, forward continuation and uniqueness of strong solutions.
In this paper, we are mainly concerned with a class of stochastic neutral functional differential... more In this paper, we are mainly concerned with a class of stochastic neutral functional differential equations of Sobolev-type with Poisson jumps. Under two different sets of conditions, we establish the existence of the mild solution by applying the Leray-Schauder alternative theory and the Sadakovskii's fixed point theorem, respectively. Furthermore, we use the Bihari's inequality to prove the Osgood type uniqueness. Also, the mean square exponential stability is investigated by applying the Gronwall inequality. Finally, two examples are given to illustrate the theory results.
In the feedback control design of real systems, an unavoidable, undesirable control performance m... more In the feedback control design of real systems, an unavoidable, undesirable control performance may occur due to the failure(s) in control components, such as actuator or/and sensor failures. Therefore, it is necessary to design controllers to achieve the desired plant performance, not only when the control components are properly operational, but also in the presence of failures. Control systems that tolerate sensor/actuator outages are called reliable control systems.
In this chapter, we consider large-scale nonlinear stochastic systems with time delay and subject... more In this chapter, we consider large-scale nonlinear stochastic systems with time delay and subject to impulsive effects. The random noise is described by Wiener process, the time delay is finite, and the impulsive actions are applied at fixed times. The focus is on establishing uniform asymptotic stability property of the system in the mean square. In fact, stability property of large-scale systems can be achieved in different ways. As presented in Sect. 2.11, an efficient approach to deal with such a complex system is to decompose the composite (or interconnected) systems into simpler, more manageable isolated (also called uncoupled or unperturbed) subsystems at different hierarchical levels. Analyze each individual subsystem by initially ignoring the interconnection between the subsystems and then combine the available results together with interconnection, which is usually regarded as a perturbation, to draw a conclusion on the qualitative property of the composite system.
This chapter deals with exponential stability of a switched system consisting singularly perturbe... more This chapter deals with exponential stability of a switched system consisting singularly perturbed subsystems with time delay. The multiple Lyapunov functions technique with the dwell-time approach is used to establish stability properties for the switched system. 9.1 Problem Formulation Consider the following switched singularly perturbed systems with time delaẏ x(t) = f σ(t) (t, x(t), x t , z(t), z t), εż(t) = g σ (t, x(t), x t , z(t), z t), (9.1) where, for all t ≥ t 0 with t 0 ∈ R + , x ∈ R m and z ∈ R n are, respectively, the slow and fast system states or variables, 0 < ε 1 is perturbation parameter and σ : [t 0 , ∞) → S is the switching signal which is a piecewise constant function taking values in S = {1, 2,. .. , N } with N ≥ 1. If, for instance, σ = i for any i ∈ S , then system (9.1) becomeṡ x(t) = f i (t, x(t), x t , z(t), z t), t ∈ [t k−1 , t k) εż(t) = g i (t, x(t), x t , z(t), z t), t ∈ [t k−1 , t k). (9.2) For every i ∈ S , we assume that f i and g i are smooth enough to guarantee the existence of the solution of system (9.2), and f i (t, 0, 0, 0, 0) ≡ 0 and g i (t, 0, 0, 0, 0) ≡ 0 (for all t) to ensure that system (9.2) has the trivial solution (x z) T ≡ (0 T 0 T). Let x t = x(t + θ) be the delayed state where θ ∈ [−τ , 0] with
In this chapter, we consider nonlinear stochastic impulsive systems with time delay. Particularly... more In this chapter, we consider nonlinear stochastic impulsive systems with time delay. Particularly, the time delay here is finite; the stochastic noise is represented by a Wiener process, and the impulses are state-independent and are of types diminishing and unbounded in total.
This chapter deals with some stability notions for impulsive-switched systems with time-delayed s... more This chapter deals with some stability notions for impulsive-switched systems with time-delayed singularly perturbed subsystems. The technique of multiple Lyapunov functions and dwell-time switching signal are used to analyze the stability properties. As will be seen, the impulses can contribute to obtain stability properties even when the system consists of only unstable subsystems.
Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016
This paper addresses stochastic control system of differential equations with piecewise constant ... more This paper addresses stochastic control system of differential equations with piecewise constant arguments (SEPCA ). The piecewise constant arguments are of delay type. The system is viewed as a hybrid (or particularly switched) system . This approach motivates the applicability of the classical theory of ordinary differential equations, but not of functional differential equations, and the design of a switching law. The main theme of this work is to establish the problems of input-to-state stabilization (ISS ), and H ∞ performance for a class of an uncertain control SEPCA. To analyze these result, a common Lyapunov function together with the techniques of differential inequalities and Razumikhin condition is used. A numerical example with simulations is presented to clarify the validity of the proposed theoretical approaches.
Springer proceedings in mathematics & statistics, 2015
This chapter deals with large-scale nonlinear delay stochastic systems where the system states ar... more This chapter deals with large-scale nonlinear delay stochastic systems where the system states are subject to impulsive effects and perturbed by some disturbance input having bounded energy. The interest is to develop a comparison principle and establish input-to-state stability (ISS) in the mean square (m.s.) using vector Lyapunov function and Razumikhin technique. Impulses are being viewed as perturbation to stable systems, and they have a stabilizing role to unstable systems.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
This paper investigates exponential stability of singularly perturbed switched systems with time ... more This paper investigates exponential stability of singularly perturbed switched systems with time delay. The multiple Lyapunov functions technique and dwell time approach are used to establish stability criteria for a switched system consisting of both stable and unstable subsystems. Examples are presented to illustrate the criteria.
This paper addresses stochastic hybrid systems, particularly switched and impulsive systems. The ... more This paper addresses stochastic hybrid systems, particularly switched and impulsive systems. The systems under consideration are linear and non-linear continuous with/without time delay, and with/without external force. The importance of using such systems and the discrepancies between hybrid and non-hybrid systems are presented. The objective of this paper is to survey recent developments on some of the important qualitative properties such as stability, stabilisation, input-to-state stability and state estimation along with the challenges that might arise when taking hybridness into account. These properties are mainly developed by using the direct method of Lyapunov or Lyapunov–Razumikhin if time delay is taken into account. Several examples with simulations are presented to further clarify the results introduced in this paper.
ABSTRACT This paper studies time-delayed switched systems that include both stable and unstable m... more ABSTRACT This paper studies time-delayed switched systems that include both stable and unstable modes. By using multiple Lyapunov-functions technique and a dwell-time approach, several criteria on exponential stability for both linear and nonlinear systems are established. It is shown that by suitably controlling the switching between the stable and unstable modes, exponential stabilization of the switched system can be achieved. Some examples and numerical simulations are provided to illustrate our results.
Springer proceedings in mathematics & statistics, 2018
This paper addresses the exponential stability problem for discrete impulsive switched singular s... more This paper addresses the exponential stability problem for discrete impulsive switched singular systems with time delay where the impulsive effects occur as a result of switching among the subsystems. Some sufficient conditions on the exponential stability of the system are established. The stability conditions are investigated by using the multiple Lyapunov functions along with the average dwell time switching signal and by resorting the Halanay lemma. Finally, numerical examples with simulations are provided.
This chapter deals with the problem of designing a robust reliable decentralized control for impu... more This chapter deals with the problem of designing a robust reliable decentralized control for impulsive large-scale systems (ILSS) with admissible uncertainties in the system states. Then, the same idea is carried over to design reliable observers to estimate the states of the above systems. The faulty actuator/sensor outputs are assumed to be zero. The reliability analysis is achieved by using a scalar Lyapunov function.
In this chapter, we address stochastic impulsive systems with time delay, where the impulse times... more In this chapter, we address stochastic impulsive systems with time delay, where the impulse times are state-dependent. Using Ito calculus, we develop the essential foundation of the theory of the mentioned system, namely local and global existence, forward continuation and uniqueness of strong solutions.
In this paper, we are mainly concerned with a class of stochastic neutral functional differential... more In this paper, we are mainly concerned with a class of stochastic neutral functional differential equations of Sobolev-type with Poisson jumps. Under two different sets of conditions, we establish the existence of the mild solution by applying the Leray-Schauder alternative theory and the Sadakovskii's fixed point theorem, respectively. Furthermore, we use the Bihari's inequality to prove the Osgood type uniqueness. Also, the mean square exponential stability is investigated by applying the Gronwall inequality. Finally, two examples are given to illustrate the theory results.
In the feedback control design of real systems, an unavoidable, undesirable control performance m... more In the feedback control design of real systems, an unavoidable, undesirable control performance may occur due to the failure(s) in control components, such as actuator or/and sensor failures. Therefore, it is necessary to design controllers to achieve the desired plant performance, not only when the control components are properly operational, but also in the presence of failures. Control systems that tolerate sensor/actuator outages are called reliable control systems.
In this chapter, we consider large-scale nonlinear stochastic systems with time delay and subject... more In this chapter, we consider large-scale nonlinear stochastic systems with time delay and subject to impulsive effects. The random noise is described by Wiener process, the time delay is finite, and the impulsive actions are applied at fixed times. The focus is on establishing uniform asymptotic stability property of the system in the mean square. In fact, stability property of large-scale systems can be achieved in different ways. As presented in Sect. 2.11, an efficient approach to deal with such a complex system is to decompose the composite (or interconnected) systems into simpler, more manageable isolated (also called uncoupled or unperturbed) subsystems at different hierarchical levels. Analyze each individual subsystem by initially ignoring the interconnection between the subsystems and then combine the available results together with interconnection, which is usually regarded as a perturbation, to draw a conclusion on the qualitative property of the composite system.
This chapter deals with exponential stability of a switched system consisting singularly perturbe... more This chapter deals with exponential stability of a switched system consisting singularly perturbed subsystems with time delay. The multiple Lyapunov functions technique with the dwell-time approach is used to establish stability properties for the switched system. 9.1 Problem Formulation Consider the following switched singularly perturbed systems with time delaẏ x(t) = f σ(t) (t, x(t), x t , z(t), z t), εż(t) = g σ (t, x(t), x t , z(t), z t), (9.1) where, for all t ≥ t 0 with t 0 ∈ R + , x ∈ R m and z ∈ R n are, respectively, the slow and fast system states or variables, 0 < ε 1 is perturbation parameter and σ : [t 0 , ∞) → S is the switching signal which is a piecewise constant function taking values in S = {1, 2,. .. , N } with N ≥ 1. If, for instance, σ = i for any i ∈ S , then system (9.1) becomeṡ x(t) = f i (t, x(t), x t , z(t), z t), t ∈ [t k−1 , t k) εż(t) = g i (t, x(t), x t , z(t), z t), t ∈ [t k−1 , t k). (9.2) For every i ∈ S , we assume that f i and g i are smooth enough to guarantee the existence of the solution of system (9.2), and f i (t, 0, 0, 0, 0) ≡ 0 and g i (t, 0, 0, 0, 0) ≡ 0 (for all t) to ensure that system (9.2) has the trivial solution (x z) T ≡ (0 T 0 T). Let x t = x(t + θ) be the delayed state where θ ∈ [−τ , 0] with
In this chapter, we consider nonlinear stochastic impulsive systems with time delay. Particularly... more In this chapter, we consider nonlinear stochastic impulsive systems with time delay. Particularly, the time delay here is finite; the stochastic noise is represented by a Wiener process, and the impulses are state-independent and are of types diminishing and unbounded in total.
This chapter deals with some stability notions for impulsive-switched systems with time-delayed s... more This chapter deals with some stability notions for impulsive-switched systems with time-delayed singularly perturbed subsystems. The technique of multiple Lyapunov functions and dwell-time switching signal are used to analyze the stability properties. As will be seen, the impulses can contribute to obtain stability properties even when the system consists of only unstable subsystems.
Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016
This paper addresses stochastic control system of differential equations with piecewise constant ... more This paper addresses stochastic control system of differential equations with piecewise constant arguments (SEPCA ). The piecewise constant arguments are of delay type. The system is viewed as a hybrid (or particularly switched) system . This approach motivates the applicability of the classical theory of ordinary differential equations, but not of functional differential equations, and the design of a switching law. The main theme of this work is to establish the problems of input-to-state stabilization (ISS ), and H ∞ performance for a class of an uncertain control SEPCA. To analyze these result, a common Lyapunov function together with the techniques of differential inequalities and Razumikhin condition is used. A numerical example with simulations is presented to clarify the validity of the proposed theoretical approaches.
Uploads
Papers by Mohamad Alwan