Abstract
This paper addresses the fault estimation problem for continuous-time Markovian jump systems (MJSs). Because the system is stochastic but the estimated fault is deterministic, it is not easy to study the fault estimation problem directly. To overcome this contradiction, an auxiliary system approach is proposed, where a deterministic intermediate variable is constructed by taking expectation on some stochastic variables and the error state and fault are also estimated. Moreover, based on some novel enlarging techniques, more general estimation situations about partially unknown transition rate matrix and semi-Markovian switching are firstly considered. Linear matrix inequality (LMI) conditions are given to guarantee the error states uniformly bounded. Two numerical examples are presented to illustrate the utility and advantage of established methods.
Highlights
A S it is widely known, the fault detection and isolation (FDI) problem indicates the emergence of fault by using a residual signal
FDI problem has been considered for various systems, such as deterministic systems [1]–[5], Markovian jump systems [6]–[13], switching systems [14]– [17] and networked control systems [18], [19]
An observer matching condition is usually found in references about fault estimation and not easy to be satisfied in practical systems
Summary
A S it is widely known, the fault detection and isolation (FDI) problem indicates the emergence of fault by using a residual signal. Based on the methods in [29], [30], the assumption on observer matching conditions (OMCs) could be removed Though such a condition was not necessarily needed, one cannot obtain the fault bound explicitly. The main contributions are clarified below: 1) An auxiliary system approach is presented to solve the fault estimation problem, while the contradiction between stochastic system and deterministic fault is handled; 2) The established approach is more general and includes some existing methods as special ones, which is less conservative; 3) In order to relax the precondition needing exact transition rate matrix (TRM), a general situation about partially unknown TRM is studied by applying some novel enlarging techniques to the auxiliary system. In symmetric block matrices, using “ ∗ ” as an ellipsis for the terms induced by symmetry, diag {· · ·} represents a block-diagonal matrix, and let (M ) M + M T
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