Input-output finite-time stabilization for a class of hybrid systems

The present paper extends the concept of Input–Output Finite Time Stability (IO-FTS) to a class of hybrid systems, namely Impulsive Dynamical Linear Systems, which are systems that exhibit jumps in the state trajectory. Sufficient conditions are given for the analysis of IO-FTS and for the design of a static state feedback controller, guaranteeing IO-FTS of the closed loop system. The presented results require to solve feasibility problems involving Difference/Differential Linear Matrix Inequalities, which can be solved numerically in an efficient way by using off-the-shelf optimization tools, as illustrated by the proposed examples.