Observer-based controller design of time-delay systems with an interval time-varying delay

Abstract

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.

Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays

“…Observer-based control approaches have been investigated for nonlinear dynamic systems in continuous-time as well as discrete-time domains and multiple designs have been introduced for dealing with time-varying delays (see, for example, [5,14,23,[24][25][26], etc.). Delay-independent and delay-dependent overtures of observer and controller constructions are available in the literature [27] for state estimation and stabilization of time-delay systems.…”

“…This captivates considerable attention of dynamic control researchers in both the linear and the nonlinear domains and, accordingly, various stabilization and state vector identification criteria have been presented. Observer and controller designs have been investigated for the linear delayed systems to ensure stability and robustness, see, for instant, [7,20,[22][23][24], and references therein.…”

Exponential Estimates of a Class of Time–Delay Nonlinear Systems with Convex Representations

“…As for the time-domain approach, we have found two variants: the Lyapunov-Razumikhin approach (Razumikhin, 1956), which is an adaptation of the classical Lyapunov theory, and the Lyapunov-Krasovskii one (Krasovskii, 1956), which is a natural extension of Lyapunov theory to enable the use of Lyapunov functionals (Duda, 2012). Further developments for observer design of time-delay systems can be also found (Thuan et al, 2012).…”

A separation principle for the stabilization of a class of time delay nonlinear systems

“…Therefore, output feedback stabilization of systems with delays has been the subject of numerous papers and monographs, see e. g. [10,11,12,14,19,20,23] and references therein. The effective tools of the design of the output feedback controllers are the Lyapunov-Krasovskii functional approach and the LMI based design method [3].…”