Fuzzy $\mathcal {H}_{\infty }$ Sliding Mode Control of Persistent Dwell-Time Switched Nonlinear Systems

Abstract

In this article, the fuzzy <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> sliding mode control problem for continuous-time switched nonlinear systems is investigated. The switching signal conforms to the persistent dwell-time switching mechanism. The first objective of this article is to construct a switched integral sliding surface that not only accommodates the switched nonlinear model, but ensures that the sliding mode dynamics are globally uniformly exponentially stable and have an <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 by the equivalent controller derived from the sliding surface. Another aim is to integrate the switched sliding mode control law to force the system trajectories to the sliding surface in a finite amount of time. Then, on the basis of the Lyapunov function technique, the specific form of the sliding mode control law gains is given first, and later the finite-time reachability of the sliding surface is ensured. Finally, the validity of the proposed switched sliding mode control method is validated by a numerical example.