H∞ Deconvolution Filters for Stochastic Systems with Interval Uncertainties

Abstract

This paper is concerned with the robust H ∞ deconvolution filtering problem for continuous-and discrete-time stochastic systems with interval uncertainties. The matrices of the system describing the signal transmissions are assumed to be uncertain within given intervals, and the stochastic perturbation is in the form of multiplicative Gaussian white noise with constant variance. The purpose of the addressed problem is to design a robust H ∞ deconvolution filter such that the input signal distorted by the transmission channel could recover to a specified extent γ . By using stochastic analysis techniques and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the asymptotical stability of the filtering error system. Then the filter parameters are characterized in terms of the solution to linear matrix inequalities, which can be easily solved by using available software packages. Two simulation examples are exploited to demonstrate the effectiveness of the proposed design procedures, respectively, for continuous-and discrete-time systems.

Robust L∞-induced deconvolution filtering for linear stochastic systems and its application to fault reconstruction

“…The Lemma is proved by showing the equivalence between (7) and (9). First, inequality (9) is equivalent to and is sufficiently small positive, (B.5) is in fact equivalent to (7), and the proof is completed.…”

“…The Lemma is proved by showing the equivalence between ( 7) and (9). First, inequality ( 9) is equivalent to , so that W is nonsingular.…”

“…In the recent years, the problems of H and 2 LL deconvolution [9,10] have attracted attention for linear stochastic systems governed by the Itô-type stochastic differential equations with multiplicative white noise. The variance of the multiplicative noise depends on the states or inputs of the system.…”

“…In [11], a stochastic bounded real lemma was presented in terms of LMIs, which has played an important role in H filtering design for the linear continues-time stochastic systems. Based on this important lemma, a proper filter has been proposed for the stochastic reduced-order H estimating in [12] which estimates a linear combination of state and exogenous input signals, and in [9] an H deconvolution filter has also been designed for the linear stochastic systems with state-multiplicative (state-dependent) noise and deterministic interval uncertainties. In the discrete-time case, deconvolution filtering for communication channels in which the modeling error is characterized in terms of multiplicative white noise perturbations has been designed by minimax approaches in state space setup in [13] and via a polynomial approach in [14].…”

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

“…By following a similar line as (22)- (23), and applying Schur's complement to (10), we can obtain that ELV (x t , t) < 0, and consequently, by using Definition 1 and [15], we can conclude that the trivial solution of the resulting closed-loop system (8) is robustly stochastically stable. The proof is completed.…”