New results on robust H _∞ filtering design for discrete-time piecewise linear delay systems

Abstract

This paper revisits the problem of robust H 1 filtering design for a class of discrete-time piecewise linear state-delayed systems. The state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. The parameter uncertainties are assumed to have a structured linear fractional form. Based on a novel delay-dependent piecewise Lyapunov-Krasovskii functional combined with Finsler's Lemma, a new delay-dependent sufficient condition for robust H 1 performance analysis is first derived and then the filter synthesis is developed. It is shown that by using a new linearisation technique, a unified framework can be developed so that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.

ℋ∞Control for Two-Dimensional Markovian Jump Systems with State-Delays and Defective Mode Information

“…On the other hand, the condition in (27) implies that − − T < 0, which means that is nonsingular. Thus, the controller gain can be constructed by (29). The proof is thus completed.…”

“…The driving force behind this is that MJLSs can model different classes of dynamic systems subject to random abrupt variations in their structures, for example, manufacturing systems, power systems, and networked control systems, where random failure, repairs, and sudden environment changes may occur in Markov chains [27][28][29]. It is known that MJLSs are described by a set of classical differential (or difference) equations and a Markov stochastic process (or Markov chain) [30].…”

Asymptotically necessary and sufficient stability conditions for discrete-time Takagi–Sugeno model: Extended applications of Polya's theorem and homogeneous polynomials

“…This represents a parallel result of [8] based on [7], but at the same time applies the slack matrices. It would be promising to incorporate the results in this paper into the H 1 control and networked control, for which the techniques in [22][23][24] could be applied.…”

Delay‐dependent non‐synchronized robust ℋ∞ state estimation for discrete‐time piecewise linear delay systems

“…It is known that since the delay-dependent conditions include information on the size of delays, they are generally less conservative than the delay-independent ones, especially when the size of the delays is small. More recently, based on a delay-dependent piecewise Lyapunov-Krasovskii functional, the authors in [34] studied the delay-dependent robust H ∞ filtering design for a class of discrete piecewise linear systems with time-varying state delay. It has been shown that the delay-dependent results given in [34] are much less conservative than the delay-independent ones presented in [33].…”

“…More recently, based on a delay-dependent piecewise Lyapunov-Krasovskii functional, the authors in [34] studied the delay-dependent robust H ∞ filtering design for a class of discrete piecewise linear systems with time-varying state delay. It has been shown that the delay-dependent results given in [34] are much less conservative than the delay-independent ones presented in [33]. However, it is worth pointing out that all the results given in [33,34] were obtained based on the assumption that the regions were defined by output space partitions.…”