Improved $Lcal_2$-Gain Analysis for a Class of Hybrid Systems with Applications to Reset and Event-Triggered Control

In this paper, we consider a special class of hybrid systems with periodic time-triggered jump conditions, and in which the jump map has a piecewise linear character. This hybrid systems class forms a relevant field of study as different control applications can be modeled in this hybrid system framework, including reset control and event-triggered control systems. After showing the unifying modeling character of this class of dynamical systems, we are interested in analyzing stability and L2-gain properties and we present novel conditions to do so which are significantly less conservative than the existing ones in literature. The effectiveness of the proposed modeling and analysis techniques is illustrated by means of a reset control example.