Event‐triggered finite‐time reliable control for nonhomogeneous Markovian jump systems

Abstract

Summary This article investigates the event‐triggered finite‐time reliable control problem for a class of Markovian jump systems with time‐varying transition probabilities, time‐varying actuator faults, and time‐varying delays. First, a Luenberger observer is constructed to estimate the unmeasured system state. Second, by applying an event‐triggered strategy from observer to controller, the frequency of transmission is reduced. Third, based on linear matrix inequality technique and stochastic finite‐time analysis, event‐triggered observer‐based controllers are designed and sufficient conditions are given, which ensure the finite‐time boundedness of the closed‐loop system in an H∞ sense. Finally, an example is utilized to show the effectiveness of the proposed controller design approach.

Event‐triggered finite‐time reliable filtering of Markov jump nonlinear systems subject to exponential dissipativity

“…where K 1 = diag{0.5, 0.6}, K 2 = diag{0.7, 0.9}, and the disturbance satisfying ∑ 20 k=0 w T (k)w(k) = 1.7211 < d 2 = 4. By solving the linear matrix inequalities (LMIs) ( 24)- (26) in Theorem 3, we get the values c 2 = 2.7882 and * = 0.0382, and the filter's gains are shown in Table 1.…”

“…To date, significant efforts about finite-time stability have been made. [24][25][26][27] For example, by introducing a novel partitioning scheme and using sliding-mode control method, a general framework for the finite-time stabilization issue of a class of nonlinear systems has been presented in Reference 28. Recently, the authors in Reference 29 further consider the finite-time sliding-mode control problem for a class of cyber-physical systems with Markovian jump, where randomly occurring injection attacks and ROUs are considered simultaneously.…”

“…The key of finite‐time stability is that the weighted norm of system state is kept within a certain threshold value over a specified time interval [0, N ] when a bound of initial condition is given. To date, significant efforts about finite‐time stability have been made 24‐27 . For example, by introducing a novel partitioning scheme and using sliding‐mode control method, a general framework for the finite‐time stabilization issue of a class of nonlinear systems has been presented in Reference 28.…”

Dynamic event‐triggered control for singularly perturbed systems

“…In the works of Guinaldo et al 15 and Liu et al, 16 an event‐triggered mechanism (ETM) is presented where the error has a direct bound regarding time and it is adopted in the work of Bhandari et al 17 The ETM proposed in the work of Tabuada 18 establishes linkages between measurement error and states variables in triggering condition and promises convergence to the origin. Similar structure is utilized in the work of Gao et al 19 Based on the work of Tabuada, 18 a class of time‐regularized ETM is discussed by introducing an internal dynamic variable 20 . The design of internal dynamic clocks can also be seen in the works of Mazo et al 21 and Chen et al 22 Other extensions include multi‐agent systems, 23,24 delayed system, 25 etc.…”

Robust finite‐time H∞ synchronization for uncertain discrete‐time systems with nonhomogeneous Markovian jump: Observer‐based case

“…Another type of finite‐time stability is finite‐time boundedness. It only focuses on the transient behavior of system response and is a completely different concept . More specifically, finite‐time boundedness requires that trajectories of the system remain within a prescribed range over a fixed finite‐time interval under some given initial conditions.…”