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Stability and robustness of hybrid systems using discrete-time Lyapunov techniques

The paper concerns stability analysis of hybrid systems. The main contribution is the proposed approach of discrete-time modeling of continuous-time hybrid systems. Stability analysis and robustness properties are derived from linear Lyapunov theory in discrete time. The method is especially suited for time-switched systems but can also incorporate more complex switch structures. It is also shown how periodic switch sequences fit into the analysis. The resulting problem formulations are given as linear matrix inequalities (LMIs). As an alternative to the S-procedure it is shown how to reduce conservativeness with a reduction of the LMIs state dimension when the switch regions are hyper planes. An example shows that the number of LMIs and LMI variables are reduced compared to a continuous-time approach.