Asymptotic stability of a class of linear discrete systems with multiple independent variables
The authors investigate the asymptotic stability for a class of linear shift-invariant discrete systems with multiple independent variables. They show the equivalence of this problem to the problem of robust stability of a special ordinary linear shift-varying discrete system with matrix uncertainty set defined by the coefficient matrices of the original discrete system. Then the variational method and Lyapunov's second method is used to obtain necessary and sufficient conditions for the asymptotic stability in different forms for the given class of discrete systems. A simple sufficient condition of asymptotic stability is given which becomes necessary for several special cases of the discrete system under consideration.
scientific article; zbMATH DE number 2064270