New Observer-Based Controller Design for Delayed Systems Subject to Input Saturation and Disturbances

Abstract

A new methodology to design an $${H}_{\infty }$$ observer-based controller for discrete-time delayed systems subject to input saturation and $${\mathcal {L}}_{2}$$-norm disturbances is proposed, motivated by a benchmark problem. The stabilizing observer-based controller gains are obtained from an LMI formulation using a Lyapunov–Krasovskii functional, free weighting matrices, and an effective approach to overcome the obstacle of the bilinearity. To select the most adequate controller, an iterative optimization algorithm is developed to maximize the set of admissible initial conditions. The proposed results are illustrated by a practical application using the quadruple tank process to visualize different control theory notions and phenomena in laboratory conditions.