W-Stability of Multistable Nonlinear Discrete-Time Systems

W-Stability of Multistable Nonlinear Discrete-Time Systems

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Motivated by the importance and application of discrete dynamical Football - Protective - Helmets systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems.Based on a new type stability notion of W-stability introduced by D.Efimov, the estimates Western Felt of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.