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This paper proposes a static state feedback controller design method for linear plants that are subject to polytopic uncertainty. Design specifications considered are robust H2-type disturbance attenuation and/or robust H∞-norm constraint with quadratic stabilization. First, a new parametrization of stabilizing state feedback gains and its geometric structure are investigated. Next, conditions for quadratic stabilization and the robust performances are characterized by certain functions on the parameter space. By optimizing these characteristic functions, we can obtain state feedback controllers which satisfy prescribed design specifications. Since the parameter space and the characteristic functions are convex, the use of suitable convex optimization algorithms assures convergence to global optimum. This design method is realistic and efficient for design problems which are difficult to solve analytically. Further, by optimizing maximum function of the characteristic functions, multiple specifications can be treated.

Robust Controller Design Using Parametrization of Stabilizing State Feedback Gains