Linear Quadratic Regulator: II. Robust Formulations

Abstract

The classical linear quadratic regulation problem is considered in the robust formulations where the matrices of the system and/or initial conditions are not know precisely. Several approaches are proposed where the quadratic cost is minimized against the worst-case uncertainties. Finding such controllers is performed via reducing the matrix Riccati equation with uncertainty to a single linear matrix inequality. The properties of the solutions are discussed and the comparison with previously known approaches is performed.