Positive real control problem for generalized linear plants

This paper considers the positive real control (PRC) problem for generalized linear plants without any additional assumptions. A unified approach to PRC problems based on linear matrix inequality (LMI) is proposed. It shows that this problem is solvable if and only if three LMIs have positive definite solutions. All desired PR controllers can be parameterized via the solutions of LMIs. Moreover, an existence condition and design method of low-order positive real controllers are obtained based on the above LMI approach.