Robust dissipative control for semilinear Markovian jump distributed parameter systems with time‐varying delay and incomplete transition probabilities

Abstract

This paper investigates the robust stabilization problem of semilinear Markovian jump distributed parameter systems (which are modeled by parabolic partial differential equations) with time-varying delay and incomplete transition probabilities. Based on Takagi-Sugeno (T-S) fuzzy theory, a T-S fuzzy model is obtained to describe the nonlinear systems. Furthermore, by constructing a novel Lyapunov functional candidate, several sufficient delay-dependent conditions, which ensure the considered systems stochastically stable and strictly dissipative, are established in terms of linear matrix inequalities. Finally, a fuzzy controller design approach is proposed, and two examples are presented to demonstrate the effectiveness of the designed controller.

Optimized hybrid design with stabilizing transition probability for stochastic Markovian jump systems under hidden Markov mode detector

“…For example, if we adopt the gridding technique to solve the optimization problem (20) and ( 21) by choosing d = 0.0001, then it is required to solve 9999 4 times of rank-constrained LMIs (10) and (11) in Example 1 and 9999 4 × 4999 4 times of rank-constrained LMIs ( 14) and ( 15) in Example 2. Clearly, the computation burden is very huge!…”

“…The primary motivation of developing MJLSs in engineering applications is that the Markov pro-cess can be applied to model the stochastic characteristics of system dynamics, for example, random parameter variations or sudden environmental disturbances [1,2]. Some typical engineering applications of MJLSs can be found in the wind turbine and networked control system [3][4][5]. Meanwhile, some existing results on study-ing the stability analysis and control/filtering issues of MJLSs have been reported in several studies [6][7][8][9][10][11] and the references therein.…”

Finite‐time dissipative control of fuzzy distributed parameter CPSs with quantization under cyber attacks

“…The extended dissipative performance has also been adopted to analyse the control synthesis of DPSs. [29][30][31][32] Moreover, the control performances are usually needed to be obtained within a limited time in practical applications. Hence, the investigation of the control strategy for distributed parameter CPSs in the finite-time interval is of practical significance.…”

On reachable set synthesis of delay Markovian jump systems under partially delay‐dependent asynchronous control

“…On the other hand, many researches on Markovian jump systems (MJSs) have made significant breakthroughs in recent decades. Because it can better describe actual systems with structure and parameter mutation, especially in the past few years, many various important top-ics on MJSs have been widely discussed, for example, stabilization [21][22][23][24][25][26][27], dissipative analysis [28][29][30][31][32], reachable set estimation [33][34][35], adaptive control [36][37][38][39], and sliding mode control [40][41][42][43][44]. Besides, Sun et al [45] have investigated the problem of disturbance attenuation for stochastic MJSs with multiple disturbances, subject to white noises and disturbances with partially known information.…”