H2 Performance Analysis and Synthesis for Discrete-Time Linear Systems with Dynamics Determined by an i.i.d. Process

TL;DR

This paper analyzes and synthesizes H2 control for discrete-time linear systems with dynamics driven by an i.i.d. process, providing tractable LMI conditions for performance analysis and controller design.

Contribution

It introduces a new H2 norm definition for such systems and derives LMI-based conditions for analysis and state-feedback controller synthesis.

Findings

LMI conditions enable numerical performance analysis

Extended results to controller synthesis

Provides a framework for systems with stochastic dynamics

Abstract

This paper is concerned with H2 control of discrete-time linear systems with dynamics determined by an independent and identically distributed (i.i.d.) process. A definition of H2 norm is first discussed for the class of systems. Then, a linear matrix inequality (LMI) condition is derived for the associated performance analysis, which is tractable in the sense of numerical computation. The results about analysis are also extended toward state-feedback controller synthesis.