A novel delay-range-dependent observer-based control approach for one-sided Lipschitz systems under measurement delays

• Published in: European journal of control 2021-09, Vol.61, p.24-39
• Main Authors: Waseem, Usama Bin, Tahir, Fatima, Rehan, Muhammad, Ahmad, Sohaira
• Format: Article
• Language: English
• Subjects: Conservatism; Control methods; Control systems design; Controllers; Convexity; Decoupling method; Delay-range-dependent stability; Derivatives; Design; Dynamic stability; Dynamical systems; Estimation-based design; Inequality; Integrals; Nonlinear control; Nonlinear systems; One-sided Lipschitz nonlinearity; Optimization; Ordinary differential equations; Wirtinger's inequality
• ISSN: 0947-3580; 1435-5671
• DOI: 10.1016/j.ejcon.2021.06.002

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.