Stable controller design for MIMO systems: an LMI approach

A unified approach to the strong stabilisation problem and the H _infin strong stabilisation problem is presented. New sufficient conditions for the existence of strongly stabilising controllers and stable H_infin controllers are derived, in a unified manner, in terms of the solvability of a positive real controller synthesis problem and a multi-objective control problem, respectively. A linear matrix inequality (LMI) technique developed by Scherer et al. is adopted to make the most use of its power to deal with the general case of the problems. Several advantages brought by the adopted LMI technique are explored. New parameterisations of stable controllers for both the problems are discussed. In particular, the parameterisations are independent of a particular method for solving strong stabilisation problems. Explicit state-space synthesis algorithms are given and numerical examples are provided to demonstrate the potential of the proposed methods