Reliable exponential filtering for singular Markovian jump systems with time‐varying delays and sensor failures

Abstract

Summary This paper deals with the problem of exponential H∞ filtering for singular Markovian jump systems with time‐varying delays subject to sensor failures. The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time‐varying delay and sensor failures is mean‐square exponentially admissible with a specified decay rate and simultaneously satisfies an H∞ performance. First, the delay interval is partitioned into m subintervals and a novel mode‐dependent stochastic Lyapunov‐Krasovskii functional is constructed. By using the reciprocally convex inequality in each subinterval, sufficient conditions of exponential H∞ performance analysis are developed for the considered filtering error system. Then, based on these conditions, the existence conditions of the desired reliable filter are derived and the filter parameters are obtained. It should be mentioned that all the results presented here are not only dependent on the time delay but also dependent on the decay rate and the partitioning size. Furthermore, all the conditions are established in terms of strict linear matrix inequalities. Finally, two numerical examples are given to illustrate the less conservatism and effectiveness of the proposed methods.

State bounding estimation for a linear continuous-time singular system with time-varying delay

“…, that is to say, x T (t)P jx (t) ≤ βu 2 α withP j = (S -T P j S -1 ) n 1 ×n 1 . Thus, the following inequality holds:…”

“…During the past years, state bounding estimation has been widely applied in control systems with actuator saturation, peak-to-peak gain minimization, and parameter estimation (see [1][2][3][4][5]). A state bounding estimation is meant to get the corresponding state bounding set which is limited by the inside and outside of the initial conditions.…”

Robust finite-time control of descriptor Markovian jump systems with impulsive

“…Their attention is focused on the design of a general filter that contains the mode-independent and mode-dependent parts to address the filtering issue and on the design of a mode-dependent nonfragile fault detection filter to guarantee the fault detection system to be stochastically admissible with an H ∞ performance index for all admissible uncertainties. In [7] a reliable filtering is designed so that the considered filtering error system in the presence of a time-varying delay and sensor failures is mean-square exponentially admissible with a specified decay rate and simultaneously satisfies an H ∞ performance.…”

Asynchronous H∞ filtering of continuous‐time Markov jump systems

“…The state estimation or filtering problem is a significant issue in signal processing and control areas . To tackle it, many effective techniques have been proposed such as the H ∞ filtering approach and the Kalman filtering method.…”

“…The state estimation or filtering problem is a significant issue in signal processing and control areas. [1][2][3] To tackle it, many effective techniques have been proposed such as the H ∞ filtering approach and the Kalman filtering method. Compared with the Kalman filtering method, H ∞ estimation shows great advantages in managing bounded disturbances with unknown statistic information.…”