Quantization-based tracking control for fuzzy singularly perturbed Markov jump systems with incomplete transition information and packet dropout

• Published in: Nonlinear dynamics Vol. 111; no. 10; pp. 9255 - 9273
• Main Authors: Guo, Fang, Luo, Mengzhuo, Cheng, Jun, Wang, Xin, Shi, Kaibo
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2023; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Co-design; Control; Control systems design; Discrete time systems; Dynamical Systems; Engineering; Fuzzy control; H-infinity control; Linear matrix inequalities; Markov analysis; Markov chains; Mathematical analysis; Measurement; Mechanical Engineering; Original Paper; Stability augmentation; Switching; Tracking control; Transition probabilities; Vibration; Singularly perturbed systems; Quantization; Piecewise-homogeneous Markov chain; Partially unknown higher-level transition probabilities matrix; Tracking control
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-08309-w

In this article, the tracking control problem for discrete-time singularly perturbed systems with a piecewise-homogeneous Markov chain subject to the effect of quantization and packet dropout is addressed based on Takagi–Sugeno (T–S) fuzzy-approximation. Firstly, the stochastic variation of mode transition probabilities with time-varying peculiarities is considered in a finite set, which is dominated by a higher-level homogeneous Markov chain. Moreover, partially unknown information in higher-level transition probabilities (HTPs) matrix is resolved by constructing a unified framework, which covers the stochastic switching and arbitrary switching as special cases, simultaneously. Secondly, considering the burden of network communication between components, the quantization impact and packet dropout caused by network network-induced constraints are integrated into the co-design of fuzzy tracking controller, which is mode-dependent and variation-dependent. Several criteria for the stochastic stability and H ∞ performance of the augmented system are deduced by establishing a series of linear matrix inequalities. Ultimately, two simulation examples are given to verify the practicability and effectiveness of the proposed control design schemes.