A dual optimization procedure for linear quadratic robust control problems

This paper considers the problem of choosing a single constant linear state feedback control law which produces satisfactory performance for each of several operating points of a system. The model for each operating point is assumed to be linear and the criterion for satisfactory performance is taken to be an infinite horizon quadratic cost functional. This problem is reformulated as a finite dimensional optimization over the linear feedback gains which can be readily solved using standard nonlinear optimization techniques provided a stabilizing initial value of the gains can be found. Although the direct solution of this problem will be discussed briefly, the major portion of the paper will be devoted to solution techniques when an initial stabilizing guess is not available.