Matrix Models, Supervectors and Discrete Systems

Abstract

The chapter examines the interpretation of linear, time invariant, discrete time, state space systems in terms of vector time series and matrix-based descriptions—the so-called lifted or supervector description. The approach considers dynamics on finite time intervals and releases the use of operator methodologies, the identification of the range and kernel of the system, the solution of the linear quadratic tracking control problem and important links between operator properties and properties of the system transfer function matrix.