This paper addresses the stability problem of a class of nonlinear switched systems with partitioned state-space and state-dependent switching. In lieu of the Carathéodory solutions, the general Filippov solutions are considered. This encapsulates solutions with infinite switching in finite time. Based on the theory of differential inclusions, a Lyapunov stability theorem is brought forward. Th...

In this paper, the global asymptotic stability of second-order neutral type Cohen-Grossberg neural networks with time-varying delays are investigated. First, by choosing properly variable substitution the system is transformed to first-order differential equation. Second, some sufficient conditions which can ensure the existence and global asymptotic stability of equilibrium point for the syste...

Many stability results in the theory of stochastic hereditary systems and their applications were obtained by construction of appropriate Lyapunov functionals. One general method of Lyapunov functionals construction was proposed and developed by the authors during last decade for stability investigation of deterministic and stochastic functional-differential and difference equations. In this pa...

A class of global Lyapunov functions is revisited and used to resolve a long-standing open problem on the uniqueness and global stability of the endemic equilibrium of a class of multi-group models in mathematical epidemiology. We show how the group structure of the models, as manifested in the derivatives of the Lyapunov function, can be completely described using graph theory.

We provide necessary and sucient conditions for psi-conditional as-ymptotic stability of the solution of a linear matrix Lyapunov system and sucientconditions for psi -conditional asymptotic stability of the solution of a rst ordernon-linear matrix Lyapunov system X0 = A(t)X + XB(t) + F(t;X).

In this paper, a chattering-free sliding-mode control is mainly proposed in a second-order discrete-time system. For achieving this purpose, firstly, a suitable control law would be derived by using the discrete-time Lyapunov stability theory and the sliding-mode concept. Then the input constraint is taken into account as a saturation function in the proposed control law. In order to guarantee ...

this paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. in this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. the robust controller is designed on the basis of fractional lyapunov stability theory. furthermore, the effects of model uncertainti...

This chapter presents a new face recognition system comprising of feature extraction and the Lyapunov theory-based neural network. It first gives the definition of face recognition which can be broadly divided into (i) feature-based approaches, and (ii) holistic approaches. A general review of both approaches will be given in the chapter. Face features extraction techniques including Principal ...

This paper is concerned with the robust stability for uncertain systems with time-varying delay and nonlinear perturbations. Using Lyapunov stability theory and free weighting matrix techniques, delaydependent stability criterion is derived in terms of linear matrix inequality without applying any bounding techniques. Finally, numerical example is given to illustrate the improvement over some e...