Finite-Time Boundedness and H∞ Control for Affine Switched Systems

Abstract EN

For affine switched systems, the existence of multiple equilibria is related to subsystems owing to the affine terms, which makes asymptotic and finite-time stability analysis nontrivial.

In this paper, the problems of finite-time boundedness (FTB) analysis and stabilization are addressed for affine switched systems, and several definitions and sufficient conditions are proposed to study FTB and H∞ performance.

At first, the definition of FTB for affine switched systems is improved concerning the affine terms and multiple equilibria.

Based on the FTB definition, sufficient conditions ensuring finite-time boundedness for affine switched systems under a prespecified state boundary are given.

Then the results are extended to solve H∞ finite-time boundedness problem, in which the H∞ controllers are designed to guarantee the finite-time boundedness of affine switched system with H∞ performance.

In our investigation, average dwell-time approach is employed to study the time-dependent constrained switching case.

Finally, several numerical examples are given to illustrate the effectiveness of the proposed results.