Fuzzy $\mathcal {H}_{\infty }$ Control of Semi-Markov Jump Singularly Perturbed Nonlinear Systems With Partial Information and Actuator Saturation

This article focuses on the fuzzy
$\mathcal {H}_{\infty }$
control problem for a class of semi-Markov jump singularly perturbed nonlinear systems with actuator saturation. Nonlinearities in the underlying systems are tackled with the Takagi–Sugeno fuzzy model. As distinct from the previous achievements, the case that the semi-Markov kernel with partially known information is taken into account such that the underlying systems can be extended to a wider scope. Given that actuator saturation is ubiquitous in engineering systems, the convex hull method is embraced to address this circumstance. To reduce the conservativeness of the obtained results, on the basis of Lyapunov stability theory and LaSalle's invariance principle, some criteria related to the sojourn time are presented. Next, the mean-square exponential stability of the underlying system is obtained based on the derived results. Finally, further experiment to verify the feasibility of the proposed methodology is given by a tunnel diode circuit model.