Stabilization of Some Classes of Uncertain Control Systems with Evaluation of Admissible Disturbance for the Object Matrix

The system = M (·) x + e n u , u = s T x , where M (·) ∈ , s ∈ R n , and the pair ( M (·), e n ) is completely controllable, is considered. The elements of the matrix M (·) are nonanticipating functionals of arbitrary nature. The object matrix is assumed to have the form M (·) = A (·) + D (·), where A (·) is a generalized Frobenius matrix and D (·) is a disturbance matrix. The quadratic Lyapunov function V ( x ) with a constant matrix of special form and the number α > 0, which is an estimate for under the condition D (·) = 0, are brought into consideration. For an arbitrary α > 0, the vector s and the estimate of the norm of the matrix D (·) are determined in such a way that the system under consideration becomes globally exponentially stable.