Positive Real Synthesis of Networked Control System An LMI Approach

TL;DR

This paper develops a method for analyzing and synthesizing positive real controllers for discrete-time networked control systems using LMIs, ensuring stability and passivity.

Contribution

It introduces a new LMI-based approach for positive real synthesis in NCS, providing conditions for controller design via coupled LMIs.

Findings

Existence of mode-dependent positive real controllers under LMI conditions

Controller construction from LMI solutions

Guarantees stability and passivity of NCS

Abstract

This paper presents the positive real analysis and synthesis for Networked Control Systems (NCS) in discrete time. Based on the definition of passivity, the sufficient condition of NCS is given by stochastic Lyapunov functional. The controller via state feedback is designed to guarantee the stability of NCS and closed-loop positive realness. It is shown that a mode-dependent positive real controller exists if a set of coupled linear matrix inequalities has solutions. The controller can be then constructed in terms of the solutions.