Randomized and deterministic algorithms for stabilization with fixed order controllers

In this paper, we study fixed order stabilizing controllers for single-input single-output plants. Following previous research, the controller parameters are classified into two types: (computationally) tractable and intractable parameters. First, we propose to use randomized algorithms to find the intractable parameters. Then, we present a deterministic method to compute the values of tractable parameters. This technique is based on matrix inversion and it is shown to be superior (from the computational complexity point of view) to existing methods based on linear programming.