H \(_\infty \) Control of Nonlinear Systems Case

In this chapter, the \(H_{\infty }\) control problem for nonlinear hidden Markov jump singularly perturbed systems (HMJSPSs) with complex probability information is addressed based on the T-S fuzzy model. The complex probability information encompass both the transition probabilities matrix (TPM) and observation probability matrix (OPM). A novel hidden Markov model (HMM) is employed to describe these partial information problems, in which certain elements remain unidentified. Additionally, criteria pertaining to \(H_{\infty }\) performance analysis and the desired HMM-based controller design method are obtained. Finally, two examples are provided to demonstrate the practical application of the HMM-based asynchronous controller design procedures.