On The Determination Of Parametric Linear Quadratic Regulators for Parametric Systems
This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant (LTI) systems affected by parameters. In particular, the paper considers the problem of determining a parametric controller that minimizes the worst-case cost over the set of admissible parameters. It is shown that a candidate for such a controller can be obtained by solving a convex optimization problem with linear matrix inequality (LMI) constraints. This candidate is guaranteed to approximate arbitrarily well the sought controller by sufficiently increasing the size of the LMIs. Moreover, a condition for establishing the optimality of the found candidate is provided. Some numerical examples illustrate the proposed methodology.