Finite-time Control Design For Several Classes Nonlinear Descriptor Systems

With the rapid development of science and technology,researches on nonlinear systems have become a hot topic in the international control field.In many complex nonlinear systems,such as circuit systems and electric systems,the constrained mechanical systems and robot systems,chemical process,population model and economic model,etc.,are coupled with several dynamic subsystems and static subsystems.Such systems are called nonlinear descriptor systems.However,in some practical applications,this paper mainly considers the behavior of the system in a period of time and discusses the stability of the system within a finite(possibly short)interval.Due to the difficulty in designing the finite-time controller for nonlinear descriptor systems,few research results have been obtained,while nonlinear descriptor systems are widely applied in practical systems,such as missile systems,robot control systems,communication network systems,ATM network control systems,etc..Therefore,it is very necessary to study the finite-time stability analysis and control design of nonlinear descriptor systems.In this paper,using the structural characteristics of descriptor systems and the research methods of nonlinear systems,a suitable state\output feedback controller is designed so that the closed-loop nonlinear descriptor system is finite-time stabilization.The designed controller of this paper has the following advantages:(i)there is no restrictions for the singular matrix E,so we can design the finite-time stabilization controllers for more nonlinear descriptor system;(ii)the nonlinear vector functionf(x)of nonlinear descriptor systems need not satisfy Lipschitz conditions;(iii)the designed controllers have less conservative criteria with lower calculation complexity and more concise form.The finite-time control design problems are studied for the following several classes of nonlinear descriptor systems.1)The finite-time stabilization,finite-time H_? control,finite-time adaptive H_? control problems and its application for a class of continuous nonlinear descriptor systems are studied.Based on the structure characteristics of descriptor systems,the finite-time stabilization problems for the nonlinear descriptor system are solved with the method of state undecomposed status.Based on them,an robust controller with external disturbances and adaptive robust controller with parametric perturbations are designed,respectively.Finally,an example of the nonlinear descriptor circuit system with simulations is applied to illustrate the effectiveness of the finite-time controllers obtained in this study.2)The finite-time stabilization problems are investigated for a class of nonlinear descriptor systems with actuator saturation.Then,sufficient conditions of finite-time stabilization are given under suitable state feedback controller.Finally,the authenticity of the obtained results are showed by an example of the nonlinear descriptor circuit system.3)The finite-time stabilization and finite-time H_? control problems are considered for nonlinear discrete-time descriptor system.According to structure characteristics of the nonlinear discrete-time descriptor systems,it can be proved that the systems are causal and impulsive controllable,and suitable state feedback controllers are constructed so that nonlinear discrete-time descriptor systems are the finite-time stabilization.Finally,a population distribution problem illustrates the validity of the proposed controller of the nonlinear discrete-time descriptor system.4)The finite-time simultaneous stabilization of the case of two or more than two nonlinear descriptor systems are studied.Firstly,under output feedback,the two nonlinear descriptor systems or more than two nonlinear descriptor systems are combined with an augmented nonlinear descriptor system with an augmented dimension technique,and the sufficient condition of impulse-free is proposed.Then,based on the method of linear matrix inequalities,sufficient condition of finite-time stabilization for an augmented descriptor system is given,so it can deduce that the two nonlinear descriptor systems or more than two nonlinear descriptor systems are finite-time simultaneous stabilization.Based on them,the finite-time simultaneous stabilization is investigated for two nonlinear descriptor systems with external disturbances or actuator saturation,respectively.Finally,in order to show the effectiveness of the proposed controllers,numerical examples are given at the end of this part.