Stability and robustness for hybrid systems

Stability and robustness issues for hybrid systems are considered in this paper. Present stability results, that are extensions of classical Lyapunov theory, are not straightforward to apply in general due to two reasons. First, existing theory do not unveil how to find needed Lyapunov functions. Secondly, at some time instants it is necessary to know the values of the continuous trajectory. Because of these drawbacks, stronger conditions for stability are suggested. The search for Lyapunov functions can then be formulated as a linear matrix inequality problem. Additionally; it is shown how to obtain robustness properties. An example illustrates the results.