DESIGN OF INPUT MATRICES OF STABILIZING CONTROLLERS FOR UNCERTAIN SYSTEMS

Synthesis of stabilizing non-linear and linear controllers for uncertain systems requires that the so-called 'matching conditions' be satisfied. It is well known that an additional condition is imposed on the design if uncertainties are also present in the input matrices. This condition appears in the literature in two different, though related, forms. Roughly speaking, these conditions involve the selection of a suitable nominal input matrix. To date, no procedure for selecting this matrix is known and no existence condition for such a matrix is available. We are concerned with the problem of selecting the nominal input matrix to satisfy the two conditions. Necessary and sufficient conditions for the existence of a suitable input matrix are derived. By converting the problem of finding the suitable input matrix to a minimax problem, well-known algorithms can be used. The relations between the two forms of the condition are discussed and it is shown that if one condition is satisfied by a certain input matrix, the second condition must also be satisfied but not necessarily with the same input matrix.