Research On Problems Of Output Feedback Stabilization For Nonlinear Systems

Nonlinear phenomena are widespread in the actual production and life.All of the practical engineering control systems are nonlinear.Therefore,the research on feedback control problems of nonlinear systems is a hotspot in the field of control theory,which is of great important theoretical guiding significance and application value.It is required to research the output feedback control problem because the system states are often not all state measurable in practical engineering.In this paper,several different kinds of nonlinear systems are considered.The output feedback controllers and sampled-data controllers are designed to research the output feedback stabilization tracking problems by using the Lyapunov functional method,homogeneous method,domination method,sampled-data control method and so on.The main contents can be concluded as follows.(1)The semi-global stabilization problem for a class of nonlinear systems with state delay and uncertain nonlinear terms is addressed.Firstly,a scaling gain is introduced in order to deal with the nonlinear terms.Then,a linear output feedback controller with the scaling gain is designed based on Lyapunov-Krasovskii functional method and state observer,and the semi-global stability of the closed-loop system is ensured by adjusting the scaling gain.Finally,numerical example is given to demonstrate the feasibility of the proposed control scheme.(2)The problem of semi-global stabilization for a class of nonlinear systems with state time delay is investigated by using homogeneous domination approach.The nonlinear terms satisfy homogeneous growth condition.The homogeneous observer and output feedback controller with a scaling gain are designed according to the homogeneous property of the system and homogeneous domination approach.Using the method of Lyapunov-Krasovskii functional,the appropriate scaling gain is obtained so that the system state asymptotically converge to zero,which can ensure that the closed-loop system is semi-global stable.A numerical example shows the reasonability and effectiveness of the proposed controller design method.(3)The asymptotic stability problem for a class of nonlinear time-delay systems is researched in consideration of sampled-data control method to design sampled-data output feedback controller.The state time-delay can be divided into several intervals by using division method and each of them has the same length of the sampling period.An inductive approach is proposed to estimate the state growth,and then the sampled-data output feedback controller with a scaling gain is constructed based on state observer,which can guarantee that the closed-loop system is asymptotically stable.A numerical example is proposed to verify that the controller is valuable.(4)The global stabilization problem for a class of second order nonlinear system is studied.A bounded sampled-data controller is designed under which the closed-loop system can be transformed into a continuous time system in a certain time interval.The stability of the system is analysed via adding a power integrator and the contradiction techniques.It can be shown that the closed-loop system is globally asymptotically stable either under the bounded or unbounded controller.Finally,the effectiveness of the research results is confirmed by a numerical example.(5)The problem of global output feedback stabilization for nonlinear systems with unknown measurement sensitivity is settled by employing output feedback domination and sampleddata control strategies.The influence of sensitivity error is effectively overcome through designing the sampled-data output feedback controller together with sampled-data state observer with scaling gain,and selecting appropriate sampling period and the scaling gain,so as to realize the global stability of this class of nonlinear systems.Finally,the simulation results demonstrate the designed output feedback control scheme is available.