In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated.When switched nonlinear systems have uniform normal form an...In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated.When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law.The results of this paper are also applied to switched linear systems.展开更多
We consider the problem of stabilization near zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum.This problem was previou...We consider the problem of stabilization near zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum.This problem was previously studied in Fursikov and Shatina(2018).As it was recently revealed,the control function suggested in that work contains a term impeding transferring the stabilization construction on the 3D Helmholtz system.The main concern of this paper is to prove that this term is not necessary for the stabilization result,and therefore the control function can be changed by a proper way.展开更多
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing contr...In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.展开更多
基金Supported partially by the National Natural Science Foundation of China (Grant No 50525721)
文摘In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated.When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law.The results of this paper are also applied to switched linear systems.
基金supported by the Ministry of Education and Science of the Russian Federation (Grant No. 14.Z50.31.0037)supported by the Russian Foundation for Basic Research (Grant Nos. 15-01-03576 and 15-01-08023)
文摘We consider the problem of stabilization near zero of semilinear normal parabolic equations connected with the 3D Helmholtz system with periodic boundary conditions and arbitrary initial datum.This problem was previously studied in Fursikov and Shatina(2018).As it was recently revealed,the control function suggested in that work contains a term impeding transferring the stabilization construction on the 3D Helmholtz system.The main concern of this paper is to prove that this term is not necessary for the stabilization result,and therefore the control function can be changed by a proper way.
基金supported by the National Natural Science Foundation of China(Grant Nos.60425307,10472129 and 60221301).
文摘In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
