Novel Robust Estimation-Based Control of One-Sided Lipschitz Nonlinear Systems Subject to Output and Input Delays

• Published in: Mathematics (Basel) Vol. 12; no. 9; p. 1374
• Main Authors: Ahmad, Sohaira, Rehan, Muhammad, Ibrar, Anas, Ali, Muhammad Umair, Zafar, Amad, Kim, Seong Han
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.05.2024
• Subjects: Cartesian coordinates; Control systems design; Controllers; Convexity; Decoupling method; decoupling procedure; delay-range-dependent (DRD); Design; estimation-based control; Inequality; input and output delays; Linear matrix inequalities; Lower bounds; Neural networks; Nonlinear systems; Numerical analysis; one-sided Lipschitz; Process controls; Robust control; Simulation methods; System theory; Wirtinger’s inequality
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math12091374

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger’s inequality for the integral terms instead of the traditional and more conservative Jensen’s condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates.