A Delay-Dependent Approach to Robust H ∞ Control for Uncertain Stochastic Systems with State and Input Delays

Abstract

In this paper, the problem of delay-dependent robust H ∞ control for uncertain stochastic systems with state and input delays is investigated. The time delays are assumed to be bounded and time varying and the uncertainties are assumed to be norm bounded. By using the Lyapunov functional method, a new delay-dependent robust H ∞ control scheme is presented in terms of linear matrix inequalities (LMIs).Some numerical examples are given to illustrate the effectiveness of the proposed approach.

Delay-dependent robust H∞ control for uncertain stochastic systems with time-varying delays in state and control input

“…Our aim is to calculate the maximum allowable time delay h M , such that the system can be stabilized with disturbance attenuation level γ . In Table 3, our results on the maximum allowed delay h M for a given γ are compared with the results in Li et al 22 From Table 3, it can be shown that our results give larger delay bounds than the one in Li et al 22…”

“…Our aim is to calculate the maximum allowable time delay h M , such that the system can be stabilized with disturbance attenuation level g. In Table 3, our results on the maximum allowed delay h M for a given g are compared with the results in Li et al 22 From Table 3, it can be shown that our results give larger delay bounds than the one in Li et al 22 Case 2. Now, suppose B 1 = DB 1 (t) = E = E 1 = C 1 = D 1 = 0, the system becomes the one in Chen et al 21 To compare our results on the maximum allowable time delay h M for different given g with those in Chen et al 21 and Li et al 22 Tables 4 and 5 give the comparison results. Note that the proposed method in this article provides an H ' controller achieving much smaller g for much bigger h M , which implies that the proposed method is much less conservative than the existing results.…”

“…The stability analysis and controller design of stochastic systems has been an important topic of control theory, and a great number of results on these subjects have been reported in the literature. 14–24 For instance, by using Moon’s inequalities method, several sufficient conditions ensuring exponential stability in mean-square sense for stochastic time-delay systems were given in Chen et al 18 The problem of robust H ∞ control for uncertain stochastic systems with state delay was considered in Xu and Chen, 19 and a delay-independent H ∞ control scheme was proposed. In Chen et al, 21 Moon’s inequalities approach was applied to investigate the problem of delay-dependent robust stochastic stabilization and H ∞ control for stochastic systems with norm-bounded uncertainties and state delay.…”

“…Therefore, most existing works do not take the effect of the control input delays into account when the controllers were designed for stochastic systems. Although the problem of the H ∞ control for uncertain stochastic systems with state and input delays was studied in Li et al, 22 the time delay does not vary in a range. To the best of the authors’ knowledge, the delay range–dependent robust H ∞ control for uncertain stochastic systems with interval time-varying delay in state and control input has not been fully investigated to date, which motivates this study.…”

Fault-tolerant H∞ control for active suspension vehicle systems with actuator faults

“…In this paper, only active suspension linear systems with actuator faults are considered along with the development of a novel fault-tolerant controller design algorithm for the systems. If both unmodelled dynamics and parametric uncertainties (mass, damping coefficient, stiffness) are considered in this paper, then it is possible to deduce that the control design process will contain both parametric uncertainties, which can be modelled by normbounded uncertainties [46][47][48] or polytopic type uncertainties [3,49]. For uncertain active suspension systems with actuator faults, the fault-tolerant controller design results are also derived by using the methods proposed in this paper and the authors' previous papers [3,[46][47][48][49].…”