A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper presents a new problem of designing a robust delay-dependent PID multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a LMI approach. It formulates less conservative stability conditions using LMIs and employs Lyapunov-Krasovskii functionals, free weighting matrices, and Wirtinger inequality techniques to improve performance. The proposed approach efficiently synthesizes controller gain matrices by decoupling input and output gain matrices through a strict LMI technique.