Multi-objective control synthesis with mixed frequency small gain specifications: Youla parameterization approach

This paper considers the multi-objective synthesis problem for linear discrete-time systems with mixed frequency small gain specifications. As a starting point, the closed-loop systems are affinely parameterized with the Youla parameterization and the search of the Youla parameter is confined to finite-dimensional subspaces. Instead of starting with all arbitrary stabilizing controllers, the so-called mixed controller is used to define the Youla parameterization in order to reduce the order of the Youla parameter and achieve an acceptable closed-loop performance. Subsequently, mixed frequency small gain specifications are formulated in terms of the solvability of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the design procedure and the effectiveness of the proposed method in comparison with the existing one.