A novel delay-range-dependent observer-based control approach for one-sided Lipschitz systems under measurement delays. (September 2021)

• Record Type: Journal Article
• Authors: Waseem, Usama Bin; Tahir, Fatima; Rehan, Muhammad; Ahmad, Sohaira
• Is Part Of: European journal of control. Volume 61(2021)
• Page Start: 24
• Page End: 39
• Publication Date: 2021-09
• Subjects: Estimation-based design -- Nonlinear control -- One-sided Lipschitz nonlinearity -- Wirtinger's inequality -- Delay-range-dependent stability; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2021.06.002
• Languages: English
• ISSNs: 0947-3580

Abstract

Abstract: This paper presents the observer-based control methodology for the one-sided Lipschitz (OSL) nonlinear systems over measurement delays. A controller design method, based on the estimated states, has been provided by applying the Lyapunov-Krasovskii functional for the delayed dynamics and by inserting the OSL constraint and quadratic inner-boundedness condition. The stability of the resultant delayed dynamics is achieved through the delay-range-dependent approach, and derivative of Lyapunov functional is exploited through the Wirtinger's integral inequality approach to reduce the conservatism of the conventional Jensen's inequality scheme. Further, a necessary and sufficient solution for the main design method has been provided by employing a tedious decoupling technique to render the observer and controller gains, simultaneously, by using the recursive optimization tools. Furthermore, the solution of matrix inequality-oriented results is handled via the cone complementary linearization technique to validate the controller and observer gains through convex optimization. The effectiveness of the resultant observer-oriented control formulation for the OSL nonlinear systems under measurement delays is validated via numerical simulation examples.