Fault Estimation for Continuous-Time Markovian Jump Systems: An Auxiliary System Approach

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.

Keywords

• Fault estimation
• Markovian jump system
• semi-Markovian jump system
• stochastically intermediate variable
• intermediate estimator