Analysis and design methods of nonlinear control systems based on the model representation preserving nonlinearities

在其他方面发展了基于保持非线性的模型表示的非线性控制系统的分析和设计方法，本研究取得了以下基本理论成果：非线性描述系统的稳定性条件采用非线性描述方程作为保持非线性的模型表示，推导了具有非光滑非线性的一般描述系统的稳定性条件。Lur’型广义系统的绝对稳定条件对于由线性广义系统和静态非线性组成的Lur’型广义系统，以线性矩阵不等式（lmi）的形式导出了其绝对稳定的条件和解的存在性。线性时变系统的理论发展导致了非线性系统的理论发展。因此，将线性时变广义系统的稳定性和稳定性条件导出为线性矩阵微分不等式（LMdIs）。线性时变系统的理论发展导致了非线性系统的理论发展。因此，将线性时变广义系统的稳定性和稳定性条件导出为线性矩阵微分不等式（LMdIs）。基于具有近似误差界的有限维设计模型，推导了具有空间分布控制变量的无限维系统的控制器综合方法。此外，还解决了执行器饱和控制系统的抗干扰问题。

In other m develop analysis and design methods of nonlinear control systems based on the model representation preserving nonlinearities, this research accomplisbed the basic theoretical results as follows :1. Stability conditions for nonlinear descriptor systemsNonlinear descriptor equations were adopted as model representation preserving nonlinearities, and stability conditions were derived for general descriptor systems with non-smooth nonlinearities.2. Absolute stability conditions for Lur'e-type descriptor systemsFor Lur'e-type desciptor systems which consist of linear descriptor systems and static nonlinearities, conditions of absolute stability as well as existence of solutions were derived as linear matrix inequalities (LMIs).Theoretical development of linear time-varying systems leads to that of nonlinear systems. Thus, conditions of stability and stabilizability of linear time-varying descriptor systems were derived as linear matrix differential inequalities (LMdIs).Theoretical development of linear time-varying systems leads to that of nonlinear systems. Thus, conditions of stability and stabliralnlity of linear time-varying descriptor systems were derived as linear matrix differential inequalities (LMdIs).4. Theoretical modeling and design methods for practical systemsController synthesis methods for infinite dimensional systems with spatially distributed control variables were derived, based on finite dimensional design model with the approximation error bounds. Furthermore, disturbance rejection problem for control systems with actuator saturation were solved.