Stabilization for continuous-time switched linear systems: A mixed switching scheme

For a practical system with switching actions, it is necessary to restrict the switching frequency under the limit of its physical constraints, avoiding potential damage to the equipment. In this paper, a mixed switching scheme with both state-dependent and time-dependent functions is designed to reduce the switching frequency. First, a constant dwell-time constraint is considered and a switching logic called dwell-time min-switching rule is designed to ensure the asymptotic stability of switched system. Particularly, our result is found to be able to cover some previous results for min-switching strategy. Subsequently, a switching function with ranged dwell time scheme which means the dwell time belongs to a range other than a fixed value is taken into account. Furthermore, L₂ stabilization is studied, and the feedback controller design is incorporated into the framework of dwell-time min-switching logic. Finally, several numerical examples are presented to illustrate our results.