On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

Abstract

This paper presents the notions of exact observability and exact detectability for Markov jump linear stochastic systems of Itô type with multiplicative noise (for short, MJLSS). Stochastic Popov-Belevith-Hautus (PBH) Criterions for exact observability and exact detectability are respectively obtained. As an application, stochastic H2/H∞ control for such MJLSS is discussed under exact detectability.

Some properties of exact observability of linear stochastic systems and their applications

“…In this case, we can show that [A, C|Q] is not exactly observable because the non-trivial subspace (11) meets the condition (5).…”

“…For linear stochastic systems, several different interesting notions of observability have appeared and a rich source of references can be found in [1][2][3][4][5][6]. For linear stochastic systems, several different interesting notions of observability have appeared and a rich source of references can be found in [1][2][3][4][5][6].…”

A fault detection and isolation filter design method for Markov jump linear parameter‐varying systems

“…It can be proved that necessary and sufficient conditions that guarantee mean-square stability (see [16]) consists in the existence of a mode-dependent Lyapunov function…”

Exact detectability of linear discrete-time time-varying stochastic systems

“…In [11], the exact detectability in [25] and detectability in [5] were proved to be equivalent, and a unified treatment was proposed for detectability of Itô stochastic systems based on corresponding definitions for time-varying linear systems in [1]. Recently, the exact detectability and W-detectability have been extended to stochastic systems with Markov jumps and multiplicative noise by [14], [28], respectively, and they have been proved to be equivalent in [28].…”