A General Framework for Linear Periodic Sampled-Data Control Systems with Applications to

We present a framework for dealing with continu- ous-time periodic systems. The main tool is a lifting technique which provides a strong correspondence between continuous- time periodic systems and certain types of discrete-time time- invariant systems with infinite dimensional input and output spaces. Despite the infinite dimensionality of the input and output spaces, a lifted system has a finite-dimensional state space if the original system does. This fact permits rather constructive methods for analyzing these systems. As a demon- stration of the utility of this framework, we use it to describe the continuous time (i.e., intersample) behavior of sampled-data systems, and to obtain a complete solution to the problem of parametrizing all controllers that constrain the L*-induced norm of a sampled-data system to within a certain bound.