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A Note about Total Stability of a Class of Hybrid Systems

Robust stability results for nominally linear hybrid systems are obtained from total stability theorems for purely continuous-time and discrete-time systems. The class of hybrid systems dealt with consists of, in general, coupled continuous-time and digital systems subject to state perturbations whose nominal (i.e., unperturbed) parts are linear and time-varying, in general. The obtained sufficient conditions on robust stability are dependent on the values of the parameters defining the over-bounding functions of the uncertainties and the weakness of the coupling between the analog and digital sub-states provided that the corresponding uncoupled nominal subsystems are both exponentially stable.