Robust stabilization of polytopic discrete-time systems with time-varying state delay: A convex approach (original) (raw)

Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delaydependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach. (V.J.S. Leite). constant delay. The problem of robust filtering for discrete-time uncertain systems with delayed states is considered in some papers. Delayed state systems with norm-bounded uncertainties are studied in and with polytopic uncertainties in . In the last case the delay is time-invariant. Recently, the problem of output feedback has attracted attention and can be cited as examples of on going research. In special, presents results for precisely known systems with time-varying delay including both static output feedback (SOF) and dynamic output feedback. The conditions, however, are presented as an interactive method that relax some matrix inequalities. In time-varying delay is assumed and a nonlinear algorithm is proposed to obtain a stabilizing controller. In [24] the results of [11] are extended, including polytopic uncertainties and constant Lyapunov-Krasovskii matrices. An interesting application can be found in the context of network control system: although most of the studies in the literature on this subject deal with continuous-time models, nowadays there are some approaches using discrete-time models with delayed states . See also for a robust adaptive sliding mode control scheme applied to discrete-time systems with time-varying delay in the state and subject to norm-bounded uncertainties. In the context of discrete-time-varying systems with time-varying delay in the state, see for convex approaches to the dynamic output feedback controller design problem.