Asynchronous H_∞ filtering of continuous‐time Markov jump systems

Abstract

Summary The paper investigates the asynchronous H∞ filtering design problem for continuous‐time linear systems with Markov jump. The hidden Markov jump principle is applied to represent the asynchronous situation between the target system and the designed filter. Via a Lyapunov technique, two sufficient conditions are developed to guarantee that the filtering error system is stochastically stable with a prescribed H∞ noise attenuation level. Furthermore, three filtering design approaches are developed in the form of linear matrix inequalities. Finally, one example is provided to show the effectiveness and feasibility of the developed methods.

Adaptive Neural Network-Based Security Asynchronous Control for Uncertain Markov Jump Power Systems with Dead Zone under DoS Attack

“…Considering temporal connection of two attack actions, Markov theory is utilized to describe the stochastic DoS attack, which is more appropriate to reflect the real situation than Bernoulli process used in Reference 20. In (8), when ψ 11 = ψ 21 , the binary Markov chain becomes a Bernoulli process {φ k } with φ σk being φ k subject to Prob{φ k = 1} = ψ 11 , and Prob{φ k = 0} = 1 -ψ 11 .…”

“…To deal with this situation, the hidden Markov model (HMM) theory was applied to detect mode information and characterize the asynchronous dynamics. [8][9][10] Many HMM-based asynchronous control techniques were developed, such as the HMM-based model predictive control law and the HMM-based event trigger control law. 11,12 In Reference 13, an HMM-based asynchronous control framework was constructed for MJPSs, where system uncertainty was not considered and only state feedback control was designed assuming the availability of all precise system states.…”

Finite‐time exponentially extended dissipative filtering for singular time‐delay Markov jump systems with quantized outputs based on hidden Markov mode

“…The exploration of asynchronous filters for discrete time Markov jump neural networks can be found in References 20 and 21 and for switched systems in References 22 and 23. The corresponding counterpart of continuous time asynchronous filter was shown in Reference 24. When cyber security was concerned, Reference 25 addressed the design scheme of HMM‐based asynchronous observer for interval type‐2 fuzzy Markov jump network systems with joint deception attacks.…”

Asymptotic stability analysis of nonlinear stochastic semi‐Markov jump systems

“…Dynamical systems with Markovian switching are recognized to be very useful to model and characterize processes subject to sudden changes in external working environment and internal structural parameters, (cf. e.g., Hou, Filar and Chen; 1 Li, Liu and Cui; 2 Mao and Yuan; 3 Kwon et al; 4 Zhou and Luo, 5 Morrison; 6 Boukast and Yang; 7 Bolzern, Colaneri and Nicolao; 8,9 Fang, Loparo and Feng; 10 Goncalves, Fioravanti and Geromel; 11 Fang, Dong and Wu; 12 Vargas, Costa and Val; 13 Leth et al; 14 Teel, Subbaraman and Sferlazza 15 ). A main property of Markov processes is the lack of memory, inherited by the assumption that the distribution between two consecutive commutations is of exponential type.…”