Stabilization Control Of Crossed Triangular Nonlinear Systems With Time Delays

In the real world,many mathematical models of engineering problems such as the ball and beam system,the cart-pendulum system,can be converted into triangular nonlinear systems,which are also called lower or upper nonlinear systems.Time delay is a primary source of instability and performance degra-dation,and makes practical systems hard to control.Therefore,it is of theo-retical and practical significance to study the stabilization control for delayed triangular nonlinear systems,and in this thesis,the static gain control method is applied to study these kinds of systems.The main contents of this thesis are as follows:The first part introduces the basic concepts and properties of norm theory and Lyapunov stability theory,which will have an important role in studying the stabilization problem of triangular nonlinear systems.The second part studies the stabilization problem for a class of time-delay nonlinear systems that can be transformed into triangular nonlinear systems.· The static gain control method is successfully applied to stabilize the input-delay chained nonholonomic system.Using the input-state-scaling technique and model transformation technique,the problem of stabiliz-ing such system has been converted into that of finding two appropriate parameters such that our control objectives are satisfied.Then by means of Lyapunov-Krasovskii theory,the control strategy is given and a series of stability analysis is carried out for this kind of system.At the same time,the state and output feedback controllers are constructed here.At the end of this part,a simulation example shows the effectiveness of the designed control strategy.The third part studies the problem of stabilization control for time-delay crossed triangular nonlinear systems.· The feedback control problem of delay-free crossed triangular nonlinear systems is studied firstly.For this kind of system,we propose a unified control strategy for studying the stabilization control of such systems,and motivated by the research results of the second part,two static gain parameters are introduced at the same time to deal with heterogeneous crossed system.The high gain parameter,which is expected to be the larger the value of the gain parameter,is used to deal with the nonlinear part of the lower triangular system.The other low gain parameter hoping that the gain parameter value is as small as possible is applied to process the nonlinear part of the upper triangular system.· we then study the feedback control problem of state-delay crossed triangu-lar nonlinear systems.Based on previous research results,and by means of the Lyapunov-Krasovskii stability theorem,the asymptotic stability of the state-delay crossed nonlinear system is analyzed,and meanwhile,the delay-independent state feedback and output feedback controllers are also successfully constructed..The feedback control problem of input-delay crossed triangular nonlinear systems finally.For the input-delay crossed nonlinear system,by a specific model transformation,the crossed triangular system is successfully trans-formed into state-delay system,and the transformation does not change the structure of such crossed system.Then using the previous research results,the state and output feedback stabilization control problems of such system are studied.At the end of this part,a simulation example shows the effectiveness of the designed control strategy.