Sampled-Data Control for Asynchronously Switched Linear Systems Without MDT Constraints

In this paper, the sampled-data control problem is studied for asynchronously switched linear systems (SLSs) without minimum dwell time (MDT) constraints. The asynchronous phenomenon exists due to that the information of system mode can be acquired only at the sampling instant. First, a sufficient condition of global asymptotic stability (GAS) is presented for sampled-date switched control systems with a novel class of switching signals, which allows the switching number to be a non-affine function of time, and does not involve any point-wise bound on the switching number. Moreover, unlike the existing literature concerned with sampled-data control problem of switched systems, the MDT constraints are removed. We allow that no sampling happens between two adjacent switching instants, which makes the results more applicable to practice. Then, a sufficient condition checking the existence of sampled-data controllers is presented in terms of linear matrix inequalities (LMIs). Finally, it is shown by a boost converter circuit system that the designed sampled-data controller and switching signals can stabilize the system cooperatively.