Quadratic guaranteed cost control with robust pole placement in a disk

The paper is concerned with the design of robust state feedback controllers for a class of uncertain systems with norm bounded uncertainty, where uncertainty enters into both the state and input matrices. The controller is designed to place the closed loop poles of the uncertain system in a specified disk and guarantees an upper bound on a quadratic cost function. A procedure is given for the construction of a controller which minimises a bound on an integral quadratic performance index