Robust PID controller design with H₂ performance: Descriptor systems approach

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 controllers 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.