Finite-Time Asynchronous Fault Detection Filter Design for Conic-Type Nonlinear Semi-Markovian Jump Systems

In this work, the problem of finite-time asynchronous fault detection filter design is investigated for conic-type nonlinear semi-Markovian jump systems with time delay, missing measurements and randomly jumping fault signal. In particular, the transition probability of the semi-Markov process is considered as time-varying along with lower and upper bounds of the transition rate. Besides, the asynchronous fault detection filter is developed for semi-Markovian jump systems with specific time-varying transition probability satisfying semi-Markov process. To quantify the effects of missing measurements a stochastic variable that satisfies Bernoulli’s distribution is adopted. Furthermore, a set of sufficient conditions is derived in terms of linear matrix inequalities (LMIs) by constructing proper mode-dependent Lyapunov-Krasovskii functional such that the augmented asynchronous fault detection filtering error system is stochastically finite-time bounded with prescribed strictly
$(\mathbb {Q},\mathbb {S},\mathbb {R})-\gamma $
dissipative performance. Finally, the provided filter designs applicability and usefulness has been verified with two numerical examples.