Stability of uncertain discrete systems

The uncertain system x n+1 = A n x n, n = 0,1,2,..., is considered, where the coefficients a ij(n) of the m×m matrix A n are functionals of any nature subject to the constraints, Such systems include, in particular, switched-type systems, whose matrix A can take values in a given finite set. By using a special Lyapunov function, a bound δ ≤ δ(α 0,α *) ensuring the global asymptotic stability of the system is found. In particular, the system is stable if the last inequality is replaced by a i,j(n) = 0 for j < i. It is shown that pulse-width modulated systems reduce to the uncertain systems under consideration; moreover, in the case of a pulse-width modulation of the first kind, the coefficients of the matrix A are functions of x(n), and in the case of a modulation of the second kind, they are functionals. © 2009 Allerton Press, Inc.