A new Approach to the Multi-Objective Control of Linear Singular Perturbation Systems

The purpose of this study was to design a logic-based switching H2/H∞ state-feedback controller for continuous-time LTI singular perturbation systems. To this end, a hybrid control scheme based on a Genetic Algorithm (GA)-based supervisor is proposed which manages the combination of two controllers. A convex LMI-Based formulation of both fast and slow subsystem controllers leads to a structure which ensures a good performance in both transient and steady state phases. The stability analysis uses Lyapunov techniques, inspired from switching system theory, to prove that a system with the proposed controller remains globally stable despite the configuration (controller) changing.