Standardizability and H2-Optimization of Sampled-Data Systems with Multiple Delays

Abstract

This paper introduces the concept of generalized standard sampled-data systems with delay S_g and considers a class of multidimensional sampled-data systems that are equivalent to a certain system S_g. Such systems are called standardizable. Necessary and sufficient standardizability conditions are established. For the system S_g and standardizable systems, the H₂-optimization problem is solved using the Wiener–Hopf method. As demonstrated below, the H₂-optimization problem for a standardizable system with multiple delays is reduced to a similar problem for a standard system with single delay, which significantly simplifies calculations and qualitative analysis of the H₂-optimal system.