New Approach to Design Optimal Robust Controller for a 2-D Discrete System: OPTIMAL ROBUST CONTROLLER FOR A 2-D DISCRETE SYSTEM

Govind Prasad Pandiya; Abhay Vidyarthi; Amrita Pahadia

doi:10.56042/jsir.v84i1.8044

Authors

Govind Prasad Pandiya Department of Electronics & Communication Engineering, Lakshmi Narain College of Technology, Bhopal 462 021, Madhya Pradesh, India https://orcid.org/0000-0001-7412-010X
Abhay Vidyarthi School of Electrical & Electronics Engineering, VIT Bhopal University, Sehore 466 114, Bhopal, Madhya Pradesh, India
Amrita Pahadia Department of Electronics & Communication Engineering, Lakshmi Narain College of Technology, Bhopal 462 021, Madhya Pradesh, India

DOI:

https://doi.org/10.56042/jsir.v84i1.8044

Keywords:

Guaranteed cost control, Linear matix inequality, Robust analysis, Static state feedback, Unsymmetric lyapunov matrix

Abstract

This paper investigates the problem of ensuring the stability of an uncertain system using the unsymmetric Lyapunov function for the two-dimensional discrete system as represented by the Roesser model using the LMI approach. By employing a two-dimensional unsymmetric Lyapunov function, novel LMIs have been developed to ensure stability. The key finding of the present investigation is employing an unsymmetrical Lyapunov matrix for ensuring the stability of a two-dimensional discrete Roesser model, which is a more generalized approach to guarantee the stability of any system. This address the issues of norm-bounded parameter uncertainties, calculate the cost function using an unsymmetric Lyapunov function, and finally design the guaranteed cost controller via a static state feedback technique that not only ascertains the stability of the system but also guarantees an adequate level of performance. The advantages of this newly proposed technique are that it is LMI solvable and numerically tractable. The stability criteria have been checked and ensured based on newly developed stability conditions by considering several examples demonstrating the results effectiveness and supremacy over the previously reported techniques.