Parameter dependent state-feedback control of LPV time delay systems with time varying delays using a projection approach

Abstract

This paper is concerned with the stabilization of LPV time delay systems with time varying delays by parameter dependent state-feedback. First a stability test with H ∞ performance is given through a parameter dependent LMI. This stability test is derived from a parameter dependent Lyapunov-Krasovskii functional combined with the Jensen's inequality. From this result we derive a state-feedback existence lemma expressed through a nonlinear matrix inequality (NMI). Using a result of the paper we are able to turn this (NMI) into a bilinear matrix inequality (BMI) involving a 'slack' variable. This BMI formulation is shown to be more flexible than the initial NMI formulation and is more adequate to be solved using algorithm such as 'D-K iteration'. The controller construction is provided by two different ways. We finally discuss on the relaxation method and we show the efficiency of our method through several examples.

Design of H<inf>&#x221E;</inf> bounded non-fragile controllers for discrete-time systems

“…Although the problem remains non-convex, the latter inequality is far more simple to solve since it is possible to use simple algorithm such as D-K iteration. An example of application of such a method can be found in [8] and [9], Section 5.1.3.2.…”

“…In [8] and [9], Section 3.3. the following theorem is proved: Theorem 2.1: The following statements are equivalent:…”

“…In the following, we will consider that the matrix gain K i belongs to a particular set K i such that every matrix of K i can be written as in (8) and that K c + δK satisfies boundedness condition of its coefficients with a prescribed bound β, we have then the following proposition:…”

H∞Sampled-Data Control of LPV Systems with Time-varying Delay

“…Time delays often appear in many physical, biological and engineering systems, and the existence of time delay may cause instability. Therefore, the stability analysis and controller design problem of delayed LPV systems have been received considerable attention by man researchers [1][2][3][4][5][6]. The results of stabilization and controller design of time delay systems can be classified into two types: delay-independent and delay-dependent results.…”

Sampled-data control of linear parameter varying time-delay systems using state feedback

“…Also, there has been recent efforts devoted to the control design problem for time delay LPV systems [2], [11]. The present work is mainly inspired by the authors' recent work in [14], where the authors developed a set of linear matrix inequality (LMI)based conditions for the analysis and synthesis of state-delay LPV systems, which were less conservative compared to the existing work in the literature.…”