On the Digital Event-Triggered Stabilization of Nonlinear Asynchronous Switched Systems

In this paper, the quantized sampled-data stabilization problem of Nonlinear Asynchronous Switched (NAS) systems is studied. As a first step, semi-global practical stability results are provided for NAS systems under digitally implemented continuous-time stabilizers and any kind of switching with arbitrarily fixed dwell time. Then, by suitably exploiting the notion of Steepest Descent Switching Feedbacks (SDSFs) induced by common Lyapunov functions and the Input-to-State Stability redesign approach, a new methodology is provided for the design of robust quantized sampled-data event-triggered controllers ensuring the semi-global practical stability property of NAS systems under any kind of switching with arbitrarily fixed dwell time. An extension of the proposed control design procedure to the case of SDSFs induced by multiple Lyapunov functions is also provided. In this context, the semi-global practical stability property of the related closed-loop system is ensured under any kind of switching with sufficiently large dwell time. The stabilization in the sample-and-hold sense theory is here suitably revised and used as a tool to prove the results. In the theory here developed: (i) the presence of aperiodic sampling and of-uniform quantization in both input/output channels is considered; (ii) possible discontinuities in the functions describing the controller at hand are managed; (iii) the presence of arbitrarily large actuation disturbances and suitably bounded measurement noises is taken into account. The proposed theoretical results are validated through applications.