We consider two problems from stability theory of matrix polytopes: the existence of common quadratic Lyapunov functions and the existence of a stable member. We show the applicability of the gradient algorithm and gi...We consider two problems from stability theory of matrix polytopes: the existence of common quadratic Lyapunov functions and the existence of a stable member. We show the applicability of the gradient algorithm and give a new sufficient condition for the second problem. A number of examples are considered.展开更多
Many complex dynamical networks display synchronization phenomena. We introduce a general complex dynamical network model. The model is equivalent to a simple vector model of adopting the Kronecker product. Some synch...Many complex dynamical networks display synchronization phenomena. We introduce a general complex dynamical network model. The model is equivalent to a simple vector model of adopting the Kronecker product. Some synchronization criteria,including time-variant networks and time-varying networks,are deduced based on Lyapunov's stability theory,and they are proven on the condition of obtaining a certain synchronous solution of an isolated cell. In particular,the inner-coupling matrix directly determines the synchronization of the time-invariant network; while for a time-varying periodic dynamical network,the asymptotic stability of a synchronous solution is determined by a constant matrix which is related to the fundamental solution matrices of the linearization system. Finally,illustrative examples are given to validate the results.展开更多
文摘We consider two problems from stability theory of matrix polytopes: the existence of common quadratic Lyapunov functions and the existence of a stable member. We show the applicability of the gradient algorithm and give a new sufficient condition for the second problem. A number of examples are considered.
基金the Science and Technology R&D Program of Zhejiang Province (No.2007C33071).
文摘Many complex dynamical networks display synchronization phenomena. We introduce a general complex dynamical network model. The model is equivalent to a simple vector model of adopting the Kronecker product. Some synchronization criteria,including time-variant networks and time-varying networks,are deduced based on Lyapunov's stability theory,and they are proven on the condition of obtaining a certain synchronous solution of an isolated cell. In particular,the inner-coupling matrix directly determines the synchronization of the time-invariant network; while for a time-varying periodic dynamical network,the asymptotic stability of a synchronous solution is determined by a constant matrix which is related to the fundamental solution matrices of the linearization system. Finally,illustrative examples are given to validate the results.
