The Zero Dynamics And Stability Analysis For Nonlinear Differential-Algebraic System

In fact, linear systems in actual engineering are almost non-existent. The development of the theory of nonlinear control meets the needs of the actual situation,so that nonlinear control is of more actual significance. In a practical project, many physical models are composed by differential equations and algebraic equations. Therefore, this system (nonlinear differential algebraic system) has been concerned widely. In last few years, some research have shown that the theory of differential geometry method were a kind of effective method in analysis and design of the nonlinear control systems, as well as the Laplace transform were a very effective method for the linear system.In this paper, the development of nonlinear differential algebraic systems is firstly summarized in detail, and the basic theories of general nonlinear systems are introduced, such as coordinate transformation, feedback and so on. Further, the problem of application of zero dynamics for a class of nonlinear differential algebraic systems and the stability for a class of affine nonlinear singular systems are researched by means of the differential geometry method.(1) For a class of nonlinear differential algebraic system, the concept of zero dynamics and some conclusions are first introduced, then, by means of M derivative, the problem of application of zero dynamics is discussed, including the transformation of this system, we will obtain a form that easy to implement control—normal form.(2) The stability problems of nonlinear singular systems were studied. The concept of stability was proposed for a class of affine nonlinear singular systems, Lyapunov stability methods for the nonlinear systems were generalized to the nonlinear singular system, and the feedback stabilization problems of the nonlinear singular system were considered. The conditions under which the systems can realize feedback stabilization were obtained. By means of the vector relative degree and the normal form of the systems, for regular nonlinear singular systems, the feedback control law was constructed in which the corresponding closed loop systems can realize stabilization.