Output Feedback Stabilization For A Class Of Nontriangular Nonlinear Systems

Based on the Lyapunov stability theory,homogeneous system theory,adding a power integrator technique,adaptive control method and emulation method,this paper studies the output feedback control problem for a class of nonlinear systems with nontriangular structure.The main work of this paper is summarized as follows:1.The global output feedback control problem is considered for a class of nonlinear systems with unknown output function and nontriangular homogeneous growth condition.The output feedback controller is designed by adding a power integrator technique.Since the nonlinear term has an unknown growth rate,a dynamic gain is introduced by using the idea of adaptive control.Based on the homogeneous system theory,an appropriate update rate is selected for the dynamic gain.Combined with Barbalat lemma and reduction to absurdity,it is proved that all signals of the closed-loop system are bounded and the states of the system converge to the origin.Finally,numerical simulation is used to verify the effectiveness of the proposed control algorithm.2.The problem of adaptive output feedback control for a class of p-norm nontriangular nonlinear systems with unknown output function is considered.By adding a power integrator method and homogeneous system theory,the reduced-order observer and output feedback controller are designed.Based on the idea of homogeneous domination design,dynamic gain is introduced into the controller and observer.According to the theory of homogeneous system,the adaptive law of gain is designed.Combined with the Barbalat lemma and Lyapunov stability theory,it is proved that the closed-loop system is asymptotically stable.The simulation result validates the effectiveness of the adaptive output feedback controller.3.For a class of nontriangular nonlinear systems,the global sampled output feedback control problem is studied when the nonlinear term satisfies the linear growth condition.An adjustable gain is designed and applied to the design of discrete-time observer.The sampled output feedback controller is obtained by using the observed value at sampling time.Combining the Lyapunov function with feedback domination approach,a formula for the maximum allowable sampling period and adjustable gain is obtained.By properly selecting the controller gain parameters and sampling period,the closed-loop system is globally asymptotically stable.Finally,a numerical simulation is given to verify the effectiveness of the controller.