Realizations of 2D Continuous-Discrete Systems with Boundary Conditions over Spaces of Regulated Functions

Abstract: 2D hybrid continuous-discrete systems with boundary conditions are studied, in the general approach of the coefficient matrices and controls over spaces of functions of bounded variation or of regulated functions. The formulæ of the state and of the general response of these systems are provided, both in the case of causal and acausal cases. It is shown that the behaviour of the systems with boundary conditions is characterized by some generalized 2D semiseparable kernels. The existence of realizations of generalized 2D semiseparable kernels is proved and necessary and sufficient conditions for the minimality of the realizations are obtained.