On Sampled-Data Control of Nonlinear Asynchronous Switched Systems

In this letter, the sampled-data stabilization problem of nonlinear asynchronous switched systems is studied. In particular, a new methodology for the design of sampled-data controllers is provided for fully nonlinear asynchronous switched systems (i.e. not necessarily affine in the control inputs) described by locally Lipschitz functions. Firstly, the new notion of Steepest Descent Switching Feedback (SDSF) is introduced. Then, it is proved the existence of a suitably fast sampling such that the digital implementation of SDSFs (continuous or not) ensures the semi-global practical stability property with arbitrarily small final target ball of the related sampled-data closed-loop system under any kind of switching with arbitrarily pre-fixed dwell time. The stabilization in the sample-and-hold sense theory is used as a tool to prove the results. Possible discontinuities in the function describing the controller at hand are also managed. The case of aperiodic sampling is included in the theory here developed. The proposed theoretical results are validated through a numerical example.