New results on asynchronous H∞ control for switched discrete-time linear systems under dwell time constraint

In this technical note, the ℓ2 gain analysis and asynchronous H∞ control problems for switched discrete-time linear systems are addressed. Under the dwell time constraint, the computation of ℓ2 gains versus dwell time is viewed as an open problem. By introducing a novel dwell time dependent Lyapunov function, an LMI-based sufficient condition is proposed to solve the ℓ2 gain analysis problem. Since the derived conditions are all convex in system matrices, it is convenient to be applied into H∞ controller design. Thus, in the presence of asynchronous switching, an H∞ controller is presented to ensure the closed-loop system with a desired non-weighted H∞ performance. The proposed approach can also easily characterize the relationship between H∞ performance, dwell time and asynchronous time. Finally, several academic examples are provided to illustrate our results.