H∞ Sliding Mode Control for Nonlinear Generalized Time-delay Markov Jump Systems

doi:10.12068/j.issn.1005-3026.2024.02.001

Abstract

Abstract:

The sliding mode control problem for a class of generalized time-delay Markov jump systems with partially unknown transition rates is studied. Firstly， an integral sliding mode surface is designed for the generalized time-delay Markov jump system， and the corresponding equivalent controller is obtained. Then， a Lyapunov functional is constructed， and the sufficient conditions for the stochastic admissibly and satisfying $H ∞$ criteria $γ$ performance of the closed-loop system are obtained using linear matrix inequality method. The addition and subtraction term method and the free weight matrix are used to reduce the conservatism of the obtained results. Based on the analysis of sliding mode dynamics， a sliding mode controller is designed so that the system can reach the sliding mode surface in finite time. Finally， the feasibility of the theory is verified by numerical examples and simulations.

Key words: Markov jump system, time delay system, sliding mode control, generalized system, linear matrix inequality

CLC Number:

Dong-mei YANG, Ling-xiu DU, Chun-xia ZHU. H_∞ Sliding Mode Control for Nonlinear Generalized Time-delay Markov Jump Systems[J]. Journal of Northeastern University(Natural Science), 2024, 45(2): 153-159.

Figures/Tables 6

Fig. 1 Structure diagram of closed-loop control system

Fig. 2 State trajectories of the open-loop system x1(t )，x2(t )

Fig. 3 Trajectory of system mode r(t )

Fig. 4 State trajectories of the closed-loop system x1(t )，x2(t )

Fig. 5 Trajectories of u(t )

Fig. 6 Trajectories of the sliding mode variable s(t )

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