Finite Stabilization Controllers for Hybrid Linear Continuous-Discrete Systems

For hybrid linear autonomous continuous-discrete systems, we propose methods fordesigning two types of controllers that provide finite stabilization. The implementation of one ofthese methods, a finite stabilization state controller, is based on knowing the values of the controlsystem solution at discrete moments of time that are multiples of the quantization step. For thispurpose, an observer is constructed that makes it possible to obtain necessary solution valuesbased on the observed output signal in real time and with zero error. The second type ofregulator, a finite stabilization output controller, uses the observed output signal as a feedback,and its design is a modification of the finite state stabilization state controller by including theabove observer in its circuit.