Dissipativity of a class of uncertain systems
In the paper a system x˙ = A(·)x + B(·)u, u = S(·)x, t t0, where A(·) 2 Rnn, B(·) 2 Rnp, S(·) 2 Rpn, is considered. The elements of matrices A(·), B(·), S(·) are arbitrary functionals and are bounded. The following problem is considered: to construct such a matrix H > 0 and to define relations between the elements of matrices B(·) and S(·) such that for the given constant matrix R the inequality V (x(t)) < V (x(t0)) + t Zt0 x∗( )Rx( )d, where V (x) = x∗Hx, is valid. This problem is solved in the cases when the matrix A(·) has p elements of fixed sign, situated in either upper part of any subdiagonal or lower part of any superdiagonal. In addition it is assumed that all elements, situated to the left (or to the right) of the elements of fixed sign, are equal to zero.