Dwell time based stabilisability criteria for discrete-time switched systems

In this paper, we deal with the stabilisability problem of discrete-time switched systems constituted by all stable subsystems. We start with discrete-time switched nonlinear systems (SNSs$\mathtt {SNS}\text{s}$) and propose dwell time based criteria, in which the required Lyapunov-like functions are adapted to decrease after finite steps instead of at each step, for stabilisability, asymptotic stabilisability and exponential stabilisability, respectively. Meanwhile, the corresponding stabilising, asymptotically stabilising, exponentially stabilising switching rules can be explicitly constructed from these criteria. Afterwards, we derive two less conservative linear matrix inequality based asymptotic stabilisability criteria for discrete-time switched linear systems. In the end, two examples are given to illustrate the applicability and advantage of our extended results.