New Approach to Design Optimal Robust Controller for a 2-D Discrete System

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 twodimensional 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.