Synthesis of robust controllers for systems with integral and quadratic constraints

The problem of synthesis of fixed-order linear time-invariant controllers which stabilize a system described in terms of multiple integral quadratic constraints is considered. We show that the problem is equivalent to solving a system of bilinear matrix inequalities. In general, this leads to a non-convex optimization with many local minima, which can be searched for by using a suitable method of “local” optimization. When using the “local” approach, it is very important to choose a good starting point. In this paper, an algorithm of designing the starting point is discussed, based on a principle of separation: first, an optimal stabilizing state feedback is designed and then a best state estimate is used in the output feedback