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

TL;DR

This paper develops a robust L_infinity-induced deconvolution filtering approach for uncertain continuous-time linear stochastic systems, enabling effective sensor fault reconstruction under uncertainties and input-dependent noise.

Contribution

It introduces an improved L_infinity norm bound lemma for stochastic systems and applies it to fault reconstruction, enhancing robustness and stability in uncertain environments.

Findings

Effective fault reconstruction demonstrated in numerical examples

Improved L_infinity norm bounds for stochastic systems

Enhanced robustness in uncertain system filtering

Abstract

The problem of stationary robust L_infinity-induced deconvolution filtering for the uncertain continuous-time linear stochastic systems is addressed. The state space model of the system contains state- and input-dependent noise and deterministic parameter uncertainties residing in a given polytope. In the presence of input-dependent noise, we extend the derived lemma in Berman and Shaked (2010) characterizing the induced L_infinity norm by linear matrix inequalities (LMIs), according to which we solve the deconvolution problem in the quadratic framework. By decoupling product terms between the Lyapunov matrix and system matrices, an improved version of the proposed L_infinity-induced norm bound lemma for continuous-time stochastic systems is obtained, which allows us to realize exploit parameter-dependent stability idea in the deconvolution filter design. The theories presented are utilized for sensor fault reconstruction in uncertain linear stochastic systems. The effectiveness and advantages of the proposed design methods are shown via two numerical examples.