In this technical note, we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time-varying disturbances. By using the switched Lyapunov function method, sufficient conditions expressed as algebraic inequality constraints and linear matrix inequalities are obtained. They ensure that the nonlinear impulsive switched systems are not only exponentially stable but also satisfy the -gain condition. Based on the stability results obtained, an effective computational method is devised for the construction of switched linear stabilizing feedback controllers. A numerical example is presented to illustrate the effectiveness of the results obtained. Index Terms-Exponentially stable, linear matrix inequality (LMI), nonlinear impulsive switched systems.

The linear finite element approximation of a general linear diffusion problem with arbitrary anisotropic meshes is considered. The conditioning of the resultant stiffness matrix and the Jacobi preconditioned stiffness matrix is investigated using a density function approach proposed by Fried in 1973. It is shown that the approach can be made mathematically rigorous for general domains and used to develop bounds on the smallest eigenvalue and the condition number that are sharper than existing estimates in one and two dimensions and comparable in three and higher dimensions. The new results reveal that the mesh concentration near the boundary has less influence on the condition number than the mesh concentration in the interior of the domain. This is especially true for the Jacobi preconditioned system where the former has little or almost no influence on the condition number. Numerical examples are presented.

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This paper studies the problem of global exponential stability and exponential convergence rate for a class of impulsive discrete-time neural networks with time-varying delays. Firstly, by means of the Lyapunov stability theory, some inequality analysis techniques and a discrete-time Halanay-type inequality technique, sufficient conditions for ensuring global exponential stability of discrete-time neural networks are derived, and the estimated exponential convergence rate is provided as well. The obtained results are then applied to derive global exponential stability criteria and exponential convergence rate of impulsive discrete-time neural networks with time-varying delays. Finally, numerical examples are provided to illustrate the effectiveness and usefulness of the obtained criteria. Index TermsImpulsive discrete-time neural networks, global exponential stablity, exponential convergence rate, Halanay inequality.