Transition-Dependent Bumpless Transfer Control Synthesis of Switched Linear Systems

Abstract

This technical article is concerned with the bumpless transfer control synthesis of a class of discrete-time switched linear systems with general persistent dwell-time (PDT) switching signals. A novel piecewise transition-dependent controller facilitating the control synthesis is designed, which ensures the stability of the closed-loop system as well as the bumpless transfer at the occurrence of the switching. By imposing the given bumps limitation constraints, sufficient conditions on the existence of the controller are developed for the nominal systems. The results are extended to the case of the disturbed systems with an ensured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> -gain. Numerical examples are provided to demonstrate the effectiveness and potential of the theoretical results.