Asynchronous Control of Nonlinear Markov Jump Systems With Uncertainties Using Interval Type-2 Polynomial Fuzzy Approach
Zhaowen Xu, Zheng‐Guang Wu, Haoyi Que, Peng Jiang
Abstract
The focus of this article is to address the asynchronous control issue for a class of nonlinear Markov jump systems with parameter uncertainties. They are represented by the interval type-2 polynomial fuzzy model. A hidden Markov model is utilized to describe the asynchronous behavior between the system mode and the controller mode in a quantitative manner. This is achieved by using a joint random process, which is presented in a concise format and encompasses both spontaneous and simultaneous jumps. Further to facilitate the design flexibility and low implementation burden, the structure of the asynchronous polynomial fuzzy controller is formed based on the imperfect premise matching scheme. Facing both mismatched modes and mismatched premise variables, a joint Markov chain-based membership-function-dependent stability criteria is established by utilizing the Lyapunov–Krasovskii theory and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> performance analysis is then conducted using a sum-of-square approach. The polynomial feedback gain parameters can be readily solved by a sum of squares optimization toolbox SOSTOOLS. Finally, a numerical example is used to validate the effectiveness of our obtained results and the application potential is verified by a single-link robot arm model.