Title :
A new method for stability analysis of nonlinear discrete-time systems
Author :
Barabanov, Nikita E. ; Prokhorov, Danil V.
Author_Institution :
Dept. of Math., North Dakota State Univ., Fargo, ND, USA
Abstract :
We address the problem of global Lyapunov stability of discrete-time systems with known coefficients. We develop a method for reduction of dissipativity domain effectively testing if the system has a convex Lyapunov function. Our implementation is immediately applicable to differentiable systems with bounded nonlinearities, but the method proposed is more general and applicable to nondifferentiable systems with bounded right-hand sides. Our main application emphasis is on stability analysis of recurrent neural networks. We illustrate how to use our approach with examples.
Keywords :
Lyapunov methods; asymptotic stability; control nonlinearities; discrete time systems; nonlinear systems; recurrent neural nets; Lyapunov stability; convex Lyapunov function; discrete-time system; dissipativity domain reduction; exponential stability; nondifferentiable system; nonlinear system; recurrent neural networks; sector monotone nonlinearity; stability analysis; Lyapunov method; Mathematics; Neural networks; Nonlinear dynamical systems; Nonlinear systems; Recurrent neural networks; Stability analysis; Stability criteria; System testing; Transfer functions;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2003.820158
