Robust PID controller design with H₂ performance: Descriptor systems approach

Vojtech Veselý – Ladislav Körösi

   The paper deals with the problem to obtain robust PID controller design procedure to linear time invariant descriptor uncertain polytopic systems using descriptor system stability theory and H₂ criterion approach in the form of quadratic cost function. In the frame of Lyapunov function, H₂ quadratic cost function and Bellman-Lyapunov equation the obtained designed novel procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure, the designer could use controller with different structure like as P, PI, PID, PI-D. For PI-D controller's D-part feedback the designer could choose any available output/state derivative variables of real systems. The effectiveness of the obtained results is demonstrated on the randomly generated examples.

Keywords: robust PID controller, uncertain polytopic systems, Lyapunov function

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