Robust Estimation-Based Control for Generalized One-Sided Lipschitz Nonlinear Systems in the Presence of Output Delays

Abstract

This study presents a robust estimation-based control approach for nonlinear systems with generalized one-sided Lipschitz (OSL) conditions projected for delay measurement. A control scheme was devised for this family of nonlinear systems by deploying the Lyapunov–Krasovskii (LK) method for the delayed system and by encompassing the generalized OSL inequality without using the quadratic inner boundedness (QIB) condition to overcome the conservatism introduced by the QIB condition. The stability of the resulting system is attained by employing a delay-range-dependent technique, while the derivative of the LK functional is scouted using Wirtinger’s inequality, which shrinks the conservativeness of typical Jensen’s inequality, resulting in stability in the form of linear matrix inequalities (LMIs). Moreover, a sufficient and necessary solution for the main results was achieved through a decoupling mechanism to acquire the controller and estimator gains simultaneously using iterative optimization tools. To attenuate the effects of external disturbances on the system, the L2 gain of the error with reference to the system was computed and incorporated into the dynamics. Furthermore, the LMI-based results are handled using the cone complementary linearization (CCL) method to authenticate the controller and observer gains via convex optimization. Finally, a numerical example demonstrates the success of the presented robust observer control formation for generalized OSL nonlinear systems in the presence of output delays.

Keywords

• Robust observer-based control
• generalized one-sided Lipschitz nonlinearity
• cone complementary linearization
• Wirtinger’s inequality