Robust delay‐dependent ℋ︁_∞ control of time‐delay systems with state and input delays

Abstract

SUMMARYThis 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.

Robust delay-derivative-dependent state-feedback control for a class of continuous-time system with time-varying delays

“…u(t) is control input and ω(t) is the disturbance input. In [26], for given τ M = 0.3551 and γ = 0.000645, then the rocket motor control system is asymptotically stable.…”

“…Therefore, a better disturbance attenuation effect and smaller control feedback controller can be obtained accordingly. Furthermore, one should noted that from Table 1 and Table 2, the introduced stability criteria is less conservative than [10][11][12][13][14][15]. Example 2.…”

“…Nowadays, some important results of this issue have been made in recent years [20][21][22][23][24][25][26][27][28][29][30][31]. It is worth noting that the systems in the above literature, there still exists some conservatism for continuous-time dynamic systems with H ∞ state-feedback control and time-varying delays waiting for the further improvements.…”

“…delays, uncertainties and disturbances are employed to the stability analysis [10][11][12][13][14][15][16][17][18][19]. The delay-dependent strategies generally received much more attentions for its less conservatism than delay-independent ones, especially for the dynamic systems with a small delay range.…”

“…It is worth noting that the systems in the above literature, there still exists some conservatism for continuous-time dynamic systems with H ∞ state-feedback control and time-varying delays waiting for the further improvements. In order to obtain less conservative stability conditions, augment Lyapunov-Krasovskii functionals with the triple integral terms were employed [22][23][24][25][26]. It should be noted that, the term t t−τ x(s), Rx(s) ds always bounded as t t−τ x(s)ds, R t t−τ x(s)ds , for example, the result in [23][24] is conservatism with time delay τ is approximated with τ (t).…”