Event‐Triggered Exponential Stabilization Control of Switched Affine Systems With Zeno‐Free Behavior

Two novel methods are proposed to exclude Zeno behavior for the event‐triggered control of a class of switched affine systems (SASs) composed entirely of unstabilizable modes, within a framework without a positive minimum value of inter‐execution times. Notably, these methods no longer depend on affine terms while ensuring the asymptotic stability of a desired equilibrium point. This property can simplify the design process of event‐triggered control strategies for the stabilization problem of SASs. Unlike the existing triggering results of SASs in which only the state is triggered and updated, moreover both the state and controller gains in this article are triggered and updated, resulting in the triggering asynchronism problem. By using these two methods and Lyapunov function technology, the usual static and dynamic event‐triggering mechanisms (ETMs) can also achieve global exponential stability of the desired equilibrium point and Zeno‐free behavior of ETMs simultaneously based on the codesign of controllers and switching rule. Finally, we use an existing electric circuit example to illustrate our methods.