State feedback stabilization of uncertain linear time-delay systems: A nonlinear matrix inequality approach

The robust stabilization problem for a class of uncertain linear time-delay systems containing sector saturating actuator is considered in this paper. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters and delayed state. The delay is assumed to be constant bounded but unknown. The new criterion of delay-dependent robust stabilizability for uncertain time-delay systems is presented and the corresponding robust memoryless state feedback controller is derived in terms of the solutions of several linear matrix inequalities (LMIs). Numerical example is presented to illustrate the obtained results.

Some simple ideas on stabilization of time delay systems are exploited to find realistic robust stabilizing controllers. A discrete time controller is applied to stabilize a time delay system with a single input. Some simulation results are given and the relationship between delay duration and sampling period is discussed. >

We deal with the robust stabilizability of the class of uncertain linear time-delay systems with Markovian jumping parameters (ULTDSMJP). Under the assumption of complete access to the continuous state and the boundedness of the system's uncertainties, an independent delay sufficient conditions which guarantee the robustness stability of this class of systems are established.

the problem of robust stabilization for linear uncertain time-delay systems with nonlinear perturbation is proposed. Firstly, based on Lyapunov stability theory, the delay dependent stabilization criteria for system is developed. Secondly, robust controller is given by analyzing the stability of closed-loop system. The sufficient condition for the existence of controller is deduced. Then, the condition is further equivalent to the solvability of certain linear matrix inequality (LMI).

This paper extends some of the basic results in the area of Lyapunov (asymptotic) and finite time and practical stability to linear, discrete, time invariant time-delay systems. New definitions have been established for the latter concept of stability. Sufficient conditions for this type of stability, concerning the particular class of linear discrete time-delay systems are derived. To the best knowledge of the authors, such results have not yet been reported. Moreover, the generalization of some previous results, in the area of Lyapunov stability for the same class of systems has been also established and proven.

This paper provides sufficient conditions for both practical stability and finite time stability of linear singular continuous time delay systems which can be mathematically described as Eẋ(t) = A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> x(t) + A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> x(t - τ). Considering a finite time stability concept, new delay independent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior.

The stability of linear time-delay systems with point internal delays is difficult to deal with in practice due to the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. Stability tests for this class of systems are obtained either based on extensions of classical tests applicable to delay-free systems or on approaches within the framework of two-dimensional digital filters. Some of those two-dimensional stability tests are also proved to be useful for stability testing of a common class of linear hybrid systems.

In this paper, both problems of the stability and stabilization analysis for linear neutral time-delay systems are respectively investigated. The time-delays considered here are assumed bounded but no information to be available. Using Lyapunov functional method, delay-dependent conditions for the stability and stabilization of the systems are presented in terms of linear matrix inequality (LMI). A numerical example is given to illustrate the main results of this paper and make a comparison with the results presented in literatures

This paper is dedicated to the stability of linear time-delay system for a non small delay h. This is motivated by the fact that in some cases introducing a delay in the loop may stabilize a system. Compared to previously derived results the methodology is totally new and the resulting LMI formulas are original contributions. The derived criteria are based on Taylor series of the delay operator for which the Lagrange remainder is treated as a bounded uncertainty. A sequence of results with decreasing conservatism are obtained applying quadratic separation. An extension to robust analysis with respect to uncertain delay is also derived. A numerical example illustrates the efficiency

Robust linear controller design of uncertain discrete systems with time-varying delay

In this paper, the problem of robust stabilization for uncertain linear time-delay systems is considered. The uncertainty is assumed to be norm-bounded and appears in all the matrices of the state space model. We propose a robust stabilizability condition via dynamic memoryless state feedback in the form of linear matrix inequalities(LMIs). A control law is obtained using solutions of the LMIs.

The robust stability property of linear discrete time-delay singular systems with structured parametric uncertainties is considered. Under the assumptions that the nominal time-delay singular systems are regular, causal and stable, necessary and sufficient conditions based on μ-analysis and guardian map theory are obtained to guarantee the properties by transforming the problem into checking the nonsingularity of a class of uncertain matrices. A tight bound is obtained in terms of μ for keeping the discrete time-delay singular systems regular, causal and stable. The results can be easily extended to deal with robust D-stability problem. Two examples are given to show the feasibility of the approach.

Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

An LMI approach to guaranteed cost control of linear uncertain time-delay systems