Analysis and synthesis of discrete-time systems

This paper presents an introduction to the analysis and synthesis of sampled-data (discrete- time) systems, i.e. systems in which some or all signals can change values only at discrete values of time. The description of these systems is presented using state-space concepts. Following an introduction to linear discrete-time systems including systems where two or more samplers operate at different frequencies, here is a brief introduction to non-linear systems including the study of stability using the Second Method of Lyapunov. The latter part of the paper describes pulse-width modulated discrete systems. The final section considers the synthesis of systems designed to reach equilibrium states in the minimum number of sampling periods. The concepts discussed in the paper are illustrated with a large number of examples.