Resilient observer-based control of uncertain time-delay systems

International Journal of Systems Science, 2001

In this paper, we study the problem of designing stabilizing controllers using observers for a class of uncertain systems with state and input delays. The uncertainties are assumed to be norm bounded. By employing a Lyapunov± Krasovskii functional approach, it is proven that the closed-loop observer-based controlled system is asymptotically stable. The observer and state feedback controllers are determined by solving two linear matrix inequalities which are independent of the delay factors. A simulation example is given to illustrate the theoretical developments. Fact 1Ð Schur complement: Given constant matrices O 1 , O 2 , and O 3 where O 1ˆO T 1 and 0 < O 2ˆO T 2 then O 1 ‡ O T 3 O 1 2 O 3 < 0 if and only if

2012

This paper considers the problem of designing an observer-based output feedback controller to exponentially stabilize a class of linear systems with an interval time-varying delay in the state vector. The delay is assumed to vary within an interval with known lower and upper bounds. The time-varying delay is not required to be differentiable, nor should its lower bound be zero. By constructing a set of Lyapunov-Krasovskii functionals and utilizing the Newton-Leibniz formula, a delay-dependent stabilizability condition which is expressed in terms of Linear Matrix Inequalities (LMIs) is derived to ensure the closed-loop system is exponentially stable with a prescribed α-convergence rate. The design of an observerbased output feedback controller can be carried out in a systematic and computationally efficient manner via the use of an LMI-based algorithm. A numerical example is given to illustrate the design procedure.

Kybernetika, 2020

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International Journal of Automation and Control

This paper presents an observer-based controller design method for linear systems with interval time-varying state-delay. In this work, using a new Lyapunov-Krasovskii (LK) functional, a less conservative stabilisation criterion is derived. The Wirtinger's inequality and reciprocally convex combination lemma are exploited to develop a computationally tractable method by representing the design constraints in linear matrix inequality (LMI) framework. Numerical examples are given to demonstrate the superiority of the proposed results over the existing method.

Proceedings of the 15th IFAC World Congress, 2002, 2002

This paper investigates the controller synthesis problem of uncertain systems with time varying delays. A robust controller with delay compensation is proposed, based on Lyapunov function method. The stability criterion of the closed-loop system, which is dependent on the size of the time delay and the size of its derivative, is derived in the form of linear matrix inequalities (LMI). Examples show that the results using the method in this paper are less conservative than most existing results by other methods.

IEEE Transactions on Automatic Control, 1998

This paper examines the problem of robust stabilization via static output feedback for a class of uncertain linear state-delayed systems. Systems with a constant time-delay and subject to norm-bo'!nded parameter uncertainty in the state matrices of the 'current' and 'delayed' states and in the input matrIX are considered. We develop a method of robust stabilization based on linear matrix inequalities. The proposed design method incorporates information on the size, or an upper-bound, of the time-delay. The case of systems with polytopic uncertainty is also discussed.

International Journal of Robust and Nonlinear Control, 2011

This paper studies the design problem of robust delay-dependent H ∞ controller for a class of timedelay control systems with time-varying state and input delays, which are assumed to be noncoincident. The system is subject to norm-bounded uncertainties and L 2 disturbances. Based on the selection of an augmented form of Lyapunov-Krasovskii (L-K) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H ∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H ∞ stabilization criteria are easily extended by employing a well-known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature.

Applied Mathematics and Computation, 2008

A class of non-linear discrete-time systems with state-delay is considered. We develop an LMI-based analysis and design procedures to check primarily into the robust stability of discrete-time systems with state-delay and bounded non-linearities. Then we address the robust stabilization using nominal and resilient feedback designs. In both cases the trade-off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism. Seeking computational convenience, all the developed results are cast in the format of linear matrix inequalities (LMIs) and several numerical examples are presented throughout the paper to illustrate the feasibility of the theoretical developments.

Systems Analysis Modelling Simulation, 2002

The robust r I control problem of a class of uncertain nonlinear time-delay systems is considered in this paper. The parametric uncertainties are real time-varying and normbounded and the nonlinearities are state-dependent and cone-bounded. The delays are time-varying and bounded both in the state and at the input. We provide sucient conditions for robust stability and robust state-feedback stabilization with disturbance attenuation. Then, we establish sucient conditions for designing a linear dynamic observer-based controller which stabilizes the uncertain time-delay system and guarantees an r I -norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays. Several examples are simulated to illustrate the developed theory.

2009

This paper proposes a new approach for delay-dependent robust H ∞ stability analysis and control synthesis of uncertain systems with time-varying delay. The key features of the approach include the introduction of a new Lyapunov-Ksrasovskii functional, the construction of an augmented matrix with uncorrelated terms, and the employment of a tighter bounding technique. As a result, significant performance improvement is achieved in system analysis and synthesis without using either free weighting matrices or model transformation. Examples are given to demonstrate the effectiveness of the proposed approach.