Asynchronous Dissipative Control of Discrete-Time Fuzzy Markov Jump Systems With Dynamic State and Input Quantization

Abstract

A numerically tractable two-step approach based on backtrack and optimization searches is proposed for asynchronous quantized dissipative control of discrete-time fuzzy Markov jump systems (DFMJSs) under the networked control framework. The asynchrony of modes between the plant and controller is described by a hidden Markov model. Both dynamic state and input quantization are considered. The dynamic zooming factors of the quantizers are designed as piecewise functions with respect to their arguments to avoid division by zero. A fuzzy asynchronous quantized controller is devised to make sure that the closed-loop system is stochastically stable and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {S},\mathcal {R})$</tex-math></inline-formula> - dissipative via using a quadratic Lyapunov function and equivalent matrix transformations. Then, the iterative two-step approach is used to determine the optimal dissipativity level and the corresponding control gain and quantization parameters. Analysis and control synthesis for DFMJSs without quantization are also presented, covering some previous results as special cases. Finally, a single-link robot arm system and another numerical example are utilized to validate the present asynchronous dissipative control approaches for the quantization and non-quantization cases, respectively.