Finite Stabilization of Incompletely Controllable Hybrid LinearContinuous-Discrete Systems

For hybrid linear time-invariant continuous-discrete systems lacking the complete controllability property, we propose an approach to designing two types of controllers that provide “incomplete finite stabilization.” The implementation of one of them—a weak state feedback finite stabilization controller—is based on knowledge of the values of the control system solution at discrete moments of time, multiples of the quantization step. The second type of controller—a weak output feedback finite stabilization controller—uses the observed output signal as feedback. These controllers contain auxiliary variables described by additional discrete-time equations, and incomplete finite stabilization implies that for the closed-loop system, finite stabilization is only required for those components of the solution vector which are also components of the solution vector of the original (open-loop) system. Criteria for the existence and a method for the design of such controllers are obtained.