Abstract
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 (Q,S,R)-γ dissipative performance. Finally, the provided filter designs applicability and usefulness has been verified with two numerical examples.
Highlights
M ARKOVIAN Jump Systems (MJSs) are certain kind of hybrid dynamical systems which can be used to successfully model many practical systems such as in economic systems, aircraft control, robotics, power systems, chemical process and so on [1], [2]
We aim to establish some sufficient conditions for the existence of non-fragile asynchronous fault detection filter design that ensure the stochastic finite-time boundedness of the augmented asynchronous fault detection filtering error system (9) with strictly (Q, S, R) − γ dissipative performance
The desired non-fragile asynchronous fault detection filter system will be established in the form of (7) such that system (9) is stochastically finite-time bounded with strictly (Q, S, R) − γ dissipative performance even in the presence of time delay, missing measurements and the random jumping fault signal
Summary
M ARKOVIAN Jump Systems (MJSs) are certain kind of hybrid dynamical systems which can be used to successfully model many practical systems such as in economic systems, aircraft control, robotics, power systems, chemical process and so on [1], [2]. The dissipativitybased asynchronous filter was designed in [4] for a class of discrete-time uncertain fuzzy nonhomogeneous Markovian jump systems, where the fuzzy asynchronous full-order filter is designed to ensure the dissipative performance of the filtering error system using a triple-parameterized matrix inequality and relaxation technique. In [6], the authors investigated the robustness of the constructed filter with H∞ performance for Markovian jump systems with quantized output and unknown transfer probabilities. In [7], a novel summation inequality is adapted to design an H∞ control for Markovian jump systems with time delay
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