Hybrid discrete-continuous systems: I. stability and stabilizability

For hybrid discrete-continuous linear stationary systems, we consider the basic problems of qualitative control theory, namely, stability and stabilization. For such systems, we obtain parametric criteria for asymptotic and exponential stability ensuring a prescribed stability exponent and a rank criterion for stabilizability. We consider the problem of finding the minimum number of inputs for which the considered system is stabilizable. We suggest an effective algorithm for constructing the matrix describing the structure of the input device of a minimum-input stabilizable system. An example illustrating the results is given.