Based on the quadratic supply rate, the problem of robust dissipative control for a class of uncertain nonlinear system with sector nonlinear input is discussed. The uncertainty is described by bounded norm. It is sho...Based on the quadratic supply rate, the problem of robust dissipative control for a class of uncertain nonlinear system with sector nonlinear input is discussed. The uncertainty is described by bounded norm. It is shown that the robust dissipative control problem can be resolved for all admissible uncertainty, if there exists a storage function such that Hamilton Jacobi inequality holds. When the uncertainties of the system satisfy the matching condition, and input function within the boundedness of the sector, the closed loop system will be stronger dissipativeness, and the controller which we obtained in the paper is more flexible, because it contains an adjustable parameter for some certain range.展开更多
A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system ...A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.展开更多
In this paper, observer design for an induction motor has been investigated. The peculiarity of this paper is the synthesis of a mono-Luenberger observer for highly coupled system. To transform the nonlinear error dyn...In this paper, observer design for an induction motor has been investigated. The peculiarity of this paper is the synthesis of a mono-Luenberger observer for highly coupled system. To transform the nonlinear error dynamics for the induction motor into the linear parametric varying （LPV） system, the differential mean value theorem combined with the sector nonlinearity transformation has been used. Stability conditions based on the Lyapunov function lead to solvability of a set of linear matrix inequalities. The proposed observer guarantees the global exponential convergence to zero of the estimation error. Finally, the simulation results are given to show the performance of the observer design.展开更多
基金the National Natural Science Foundation of China(6987401569934030)and Foundation of the Education Department of Hubei Province(99A121)
文摘Based on the quadratic supply rate, the problem of robust dissipative control for a class of uncertain nonlinear system with sector nonlinear input is discussed. The uncertainty is described by bounded norm. It is shown that the robust dissipative control problem can be resolved for all admissible uncertainty, if there exists a storage function such that Hamilton Jacobi inequality holds. When the uncertainties of the system satisfy the matching condition, and input function within the boundedness of the sector, the closed loop system will be stronger dissipativeness, and the controller which we obtained in the paper is more flexible, because it contains an adjustable parameter for some certain range.
基金was supported by the Saint Petersburg State University(9.42.1045.2016)the Russian Foundation for Basic Research(15-58-53017 and 16-01-00587)the Natural Science Foundation of China(6141101096,61573030,and 61273006)
文摘A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.
文摘In this paper, observer design for an induction motor has been investigated. The peculiarity of this paper is the synthesis of a mono-Luenberger observer for highly coupled system. To transform the nonlinear error dynamics for the induction motor into the linear parametric varying （LPV） system, the differential mean value theorem combined with the sector nonlinearity transformation has been used. Stability conditions based on the Lyapunov function lead to solvability of a set of linear matrix inequalities. The proposed observer guarantees the global exponential convergence to zero of the estimation error. Finally, the simulation results are given to show the performance of the observer design.
