Stabilization of some classes of uncertain control systems with evaluation of admissible disturation for object matrix

Abstract

Consider the system x˙ = M(·)x + enu, u = sT x, where M(·) 2 Rn×n, s 2 Rn, the pair (M·), en is uniformly controlable. The elements of M(·) are nonlook-ahead functionals of arbitrary nature. The object matrix is considering in form M(·) = A(·) +D(·), where A(·) has a form of globalized Frobenious matrix, D(·) is a matrix of disturbation. Consider the square Lyapunov function V (x) with constant matrix of special form and number > 0 as estimate for ˙V for case D(·) = 0. The definition of such vector s and such estimate of norm matrix D(·) that system is globally and exponentially stable are performed for every > 0.