Output PI control of MIMO linear continuous-time systems

The paper is concerned with the problem of designing PI output feedback control laws for linear time-invariant systems. Since this problem is generally stated as a bilinear optimization problem, using standard form of Lyapunov function and symmetric positive definite slack matrices, an enhanced algorithm is introduced with incidence of a scalar tuning parameter. The solution, obtained through linear matrix inequalities and equalities formulation, also unifies the control law design LMI-based procedure. The results, offering the conditions of PI output controller existence, are illustrated with numerical examples to note effectiveness and applicability of the considered approach.