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.

本文介绍了单边 Lipschitz (OSL) 非线性系统在测量延迟上的基于观测器的控制方法。通过将 Lyapunov-Krasovskii 函数应用于延迟动力学并插入 OSL 约束和二次内有界条件，提供了一种基于估计状态的控制器设计方法。合成延迟动力学的稳定性是通过延迟范围相关的方法来实现的，并且通过 Wirtinger 的积分不等式方法利用 Lyapunov 泛函的导数来减少传统 Jensen 不等式方案的保守性。此外，通过采用繁琐的解耦技术来同时呈现观测器和控制器增益，为主要设计方法提供了必要且充分的解决方案，通过使用递归优化工具。此外，通过锥互补线性化技术处理面向矩阵不等式的结果的解决方案，以通过凸优化来验证控制器和观测器的增益。通过数值模拟示例验证了在测量延迟下的 OSL 非线性系统的最终面向观察者控制公式的有效性。