H-2 and H-infinity design of sampled-data systems using lifting. part II: Properties of systems in the lifted domain

An important class of sampled-data systems becomes time-invariant when the systems are "lifted" into an appropriate domain. The purpose of the present paper is to study some basic properties of systems represented by state sp ace equations in the lifted domain. Hidden modes, invariant zeros, and Ricc ati equations are investigated, and the connection between representations in continuous and lifted domains are clarified. The material treated here i s important for solving optimal control problems of generalized sampled-dat a systems.