This paper discusses the robust quadratic stabilization control problem for stochastic uncertain systems, where the uncertain matrix is norm bounded, and the external disturbance is a stocbastic process, Two kinds of controllers are designed, which include state feedback case and output feedback case. The conditions for the robust quadratic stabilization of stochastic uncertain systems are given via linear matrix inequalities. The detailed design methods are presented. Numerical examples show the effectiveness of our results.
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the LyapunovKarasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
This paper Investigates Hamiltonian realization of time-varying nonlinear （TVN） systems, and proposes a number of new methods for the problem. It is shown that every smooth TVN system can be expressed as a generalized Hamiltonian system if the origin is the equilibrium of the system. If the Jacooian matrix of a TVN system is nonsingular, the system has a generalized Hamiltonian realization whose structural matrix and Hamiltonian function are given explicitly. For the case that the Jacobian matrix is sin- gular; this paper provides a constructive decomposition method, and then proves that a TVN system has a generalized Hamiltonian realization if its Jacobian matrix has a non- singular main diagonal block. Furthermore, some sufficient （necessary and sufficient） conditions for dissipative Hamiltonian realization of TVN systems are also presented in this paper.
