FINITE STABILIZATION OF NOT FULLY CONTROLLED HYBRID LINEAR CONTINUOUS-DISCRETE SYSTEMS

For hybrid linear autonomous continuous-discrete systems that do not have the property of complete controllability, an approach to designing two types of controllers that provide “incomplete finite stabilization” is proposed. The implementation of one of them — a controller of weak finite state stabilization — 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 finite stabilization controller by output — uses the observed output signal as feedback. The constructed regulators contain auxiliary variables described by additional equations with discrete time, and incomplete finite stabilization implies that for a closed system, finite functions will only be required for those components of the solution vector that are components of the solution vector of the initial (open) system. Criteria for the existence of the specified regulators and a method for their design are obtained.