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

Abstract

This paper investigates the problem of delay-dependent robust H ∞ filtering design for a class of uncertain discrete-time piecewise linear state-delayed systems where state space instead of measurable output space partitions are assumed so that filter implementation may not be synchronized with plant state trajectory transitions. The state delay is assumed to be time-varying and of an interval-like type. The uncertainties are assumed to have a structured linear fractional form. The objective is to design a piecewise linear state estimator guaranteeing the asymptotic stability of the resulting filtering error system with robust H ∞ performance . Based on a new delay-dependent piecewise Lyapunov-Krasovskii functional combined with Finsler's Lemma, a novel delay-dependent robust H ∞ performance analysis result is first presented and the filter synthesis is then developed. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities, 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.

Nonsynchronized state estimation of uncertain discrete-time piecewise affine systems

“…Extensions of the current results based on more powerful relaxation techniques proposed in [15,18] are straightforward. In this way, the design conservatism should be further reduced, though the computation cost will increase.…”

Decentralized piecewise H∞ fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay

“…Moreover, the H 1 filtering does not require the exact knowledge of the statistics of the external noise signals, and it is insensitive to the exogenous disturbance. The advantages render the H 1 filtering method very appropriate to some practical applications [37,38]. To the authors' best knowledge, few attempts have been made on the decentralized H 1 filtering design for large-scale T-S fuzzy systems by using the IO approach, which motivates the research presented in this paper.…”

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

“…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].…”