Finite-time mixed H_∞ and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems

H∞ robust control based on event‐triggered sampling for hybrid systems with singular Markovian jump

“…Proof. Since the unknown matrices ΔA i have the decomposition in (9), it is easy to see that all norms of them are bounded, namely,…”

“…In particular, Markovian jump systems have recently become a rather significant topic in both theoretical research and practical applications since it can well characterize a large variety of stochastic dynamical systems subjected to abrupt changes, such as random faults, uncontrolled configuration, and unexpected events; we might also refer to previous studies [1][2][3][4][5][6] and the references therein. As a result, more and more researchers have recently devoted to study the Markovian jump systems for various perspectives including stability, 2,4 stabilization, 6 and filtering [7][8][9] and at the same time the different kinds of control strategies, including robust control, 10 slide mode control, 11 and robust H ∞ sliding mode descriptor observer, 12 have been presented and analyzed. For example, in Wu et al, 10 the problem of delay-dependent exponential stability for uncertain singular Markovian jump systems was addressed.…”

H∞ Control for Discrete‐Time Networked T‐S Fuzzy Systems with Packet Loss Based on Event‐Triggered Mechanism

“…Theorem 6. For given scalars > 0 and > 0, the nonlinear system described by (12) under the event-triggered condition (4) is mean-square stable with ∞ performance index , if there exist real symmetric positive definite matrices = > 0, > 0, and = > 0 and ∈ × ( , ∈ ) with appropriate dimensions such that ,…”

“…In [9][10][11], the ∞ control problem for a class of T-S fuzzy Markov jump systems with time-varying delay under unreliable communication relatives has been studied. In [12], it is assumed that the data transmissions between the plant and the controller are subject matter to random packet loss which satisfies Bernoulli distribution. In [13,14], the controller is designed by the PDC technique in which the controller shares the same membership functions and fuzzy premise variables with the T-S fuzzy model.…”

Finite‐Time Nonfragile Dissipative Filter Design for Wireless Networked Systems with Sensor Failures

“…Wang et al [15] studied the finite-time filter design problem of switched impulsive linear systems with parameter uncertainties and sensor induced faults by using the mode-dependent Lyapunov-like function approach. Sathishkumar et al [16] developed a finite-time ∞ filter design for a class of uncertain nonlinear discretetime Markovian jump systems represented by Takagi-Sugeno fuzzy model with nonhomogeneous jump process. The 2 Complexity asynchronous resilient controller design problem is investigated in [17], for a class of nonlinear switched systems with time delays and uncertainties in a given finite-time interval.…”