New static output feedback stabilization and multivariable PID-controller design methods for unstable linear systems via an ILMI optimization approach

The design problem of a static output feedback controller and multivariable proportional-integral-derivative (PID) controller is investigated for linear time-invariant systems (LTI). First, the static output feedback stabilization problem is taken into consideration and then an iterative linear matrix inequality (ILMI) algorithm is developed for the synthesis of the controller. Second, choosing a multivariable PID control law, the whole system is transformed into a new augmented system represented in the form of a static output feedback control system. This method allows us to convert the multivariable PID controller design problem into a static output feedback synthesis problem. Thus, the proposed ILMI algorithm can as well be utilized for the design of the multivariable PID controller. Two numerical examples are presented to illustrate a practical application of the developed methodologies.