Robust Control System Designing for an Uncertain 2D Discrete State Space Model

Abstract

newline Robust Control System Designing for an Uncertain 2D Discrete State Space Model newlineAbstract: This abstract presents a novel approach for ensuring robust stability which newlineemploying a guaranteed cost control approach in two-dimensional (2-D) discrete systems newlinebased on unsymmetric Lyapunov functions, specifically tailored for state-space models. newlineRobust stability is a paramount requirement in robust control system design to address newlineuncertainties and disturbances in real-world applications. In this study, we introduce a newlinemethod that harnesses the power of unsymmetric Lyapunov functions to enhance the newlinestability of two-dimensional discrete systems while encompassing a guaranteed cost newlinecontrol approach for performance optimization. newlineThe research commences by outlining the fundamental aspects of 2-D systems newlineand their inherent challenges in stability analysis. We emphasize the importance of newlineemploying unsymmetric Lyapunov functions, which offer a versatile means of describing newlinesystem dynamics. The core of our methodology lies in the development of a robust newlinecontrol context that integrates unsymmetric Lyapunov functions using guaranteed cost newlinecontrol approach for tailored state-space models. To assess and validate the efficacy of our proposed approach, extensive numerical optimization is led in robust control toolbox i.e., linear matrix inequalities and comparative analyses are performed against existing stability analysis techniques. The outcomes reveal the superiority of our methodology in ensuring robust stability and newlineoptimizing control performance across a range of operating conditions and in the newlinepresence of uncertainty. Furthermore, we discuss the practical applicability of this newlineapproach in diverse fields of image processing, where complex 2-D discrete systems are newlinefrequently encountered. Then discuss the significance of employing unsymmetric newlineLyapunov functions, which provide greater flexibility in representing system dynamics. newline