Pattern Classification and Construction of Lyapunov Function for Nonlinear Control Systems Using the Robust Perturbation Method

1.考虑电机的非线性特性，采用李雅普诺夫直接法对由磁阻步进电机或同步电机组成的电机系统进行了稳定性分析。结果表明，Lyapunov直接法成功地适用于非线性系统的稳定性研究。电力系统是一个复杂的工程系统。本文提出了提高电力系统暂态稳定性的两种方法。一种是基于滑模的AVR和GOV协同模糊控制技术。另一种是利用模糊控制理论的静态无功补偿技术。提出了一种构造非线性控制系统非lure型Lyapunov函数的方法。从保证的稳定性区域来看，该函数超越了Lure型Lyapunov函数。本文还提出了一种利用波波夫-李亚普诺夫方法分析摄动多机电力系统鲁棒稳定性的方法。给出了鲁棒稳定性判据，给出了系统允许扰动的一些边界。通过摄动传递函数的正实时性和Lyapunov直接方法研究了参数变化下积型非线性反馈系统的鲁棒性。该方法可获得各参数偏差的可容忍范围和产品型非线性的条件。

1.Stability analysis of motor system which consists of reluctance stepping motor or synchronous motor has been carried out by the direct method of Lyapunov, considering the nonlinearities of the motor. The results show that the direct method of Lyapunov is successfully applicable to stability studies of nonlinear systems.2.Power system is a complex engineering system. The report gives two ways of improving transient stability of power systems. One is the cooperative fuzzy control techinique of AVR and GOV based on sliding mode. The other is the static var compensator technique utilizing fuzzy control theory.3.A method of constructing non-Lure type Lyapunov function for nonlinear control system has been presented. The function surpasses the Lure type Lyapunov function from the point of view of the stability region guaranteed.4.The report also presents a method of analysing robust stability of perturbed multimachine power systems, through Popov-Lyapunov approach. Robust stability criteria are presented to derive a robustness measure which gives some bounds on allowable perturbation for the system.5.The robustness of product-type nonlinear feedback systems subjected to parameter variations has been studied through both the positive realness of perturbed transfer functions and the direct method of Lyapunov. The tolerable range of individual parameter deviations and the condition for the product-type nonlinearities can be obtained by the proposed method.