Direct H∞ Synthesis of Reduced Order Controllers for a Class of Single-Input Plants

For a class of n-th order, single-input, p-output plants, this paper proposes a simple, direct method for designing H ∞ controllers having order m ≤ n − p. To this end, the design problem is transformed into an H ∞ state feedback control for an augmented system. The conditions the plant must satisfy for this transformation to exist are derived. Once these conditions are satisfied, the controller parameters minimizing H ∞ performance are obtained just by solving a simple linear matrix inequality problem. It is shown that the method becomes more effective for multiple output systems. Two examples are considered to illustrate this approach. The first one deals with designing a first order H ∞ controller for vibration control of a fourth order quarter-car suspension system. The second one designs a first order robust H ∞ controller for a third order uncertain plant.