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

Abstract

Consider the system x'(t)=M(·)x+e_n u, u = s^T x, where M(·)x in R^{n*n}, s in R^n, the pair (M(·), e_n) 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 α > 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 α > 0.

Keywords:

uncertain systems, global and exponential stability, the square Lyapunov function