Dissipative H2/h∞ controller synthesis

In certain applications, such as the control of flexible structures, the plant transfer function is known to be psitive real. This property arises if the sensor and actuator are colocated and also dual, for example, force actuator and velocity sensor or torque actuator and angular rate sensor. In practice, the prospects for controlling such systems is quite good since, if sensor and actuator dynamics are negligible, stability is unconditionally guaranteed so long as the controller is strictly positive real [1-3]. Although there is no general theory yet available for designing positive real controllers, a variety of techniques have been proposed based on H₂ theory [4-10] and H_∞, theory [11,12]. In this paper we focus on the H₂-based positive real controller synthesis method of Lozano-Leal and Joshi [7]. In [7] it is shown that if the plant is positive real and if the error and disturbance matrices satisfy certain constraints, then the LQG controller is also positive real. This approach is appealing in practice since it requires only standard LQG synthesis techniques. Our goal in this note is to extend the synthesis technique of [7] to include an H_∞ norm bound on the closed-loop transfer function [13]. This extension thus provides the control designer with more flexibility in specifying closed-loop system performance.