Robust PI-D Controller Design for Uncertain Linear Polytopic Systems Using LMI Regions and $H_2$ Performance

The paper deals with the new design procedure for PID-D robust controller with state/output derivative feedback to stabilize the closed-loop system using linear matrix inequality (LMI) and LMI regions with common in the frame of
$H_2$
performance quadratic cost functions known as
$(Q,S,R)$
. The designed robust controller ensures robust properties of the closed loop system for linear time invariant and linear time variant gain scheduled plant descriptor systems. The robust controller design procedure is based on the extended original derivative of Lyapunov function and to obtain the convex conditions with respect to uncertainties, gain scheduled variables, and ensures that proposed new method guarantees less conservativeness to the design procedure we have introduced using the auxiliary matrices. The obtained results should be utilized to design power system stabilizer for synchronous generators and so on. The obtained robust PI-D controller with output and state/output derivative feedback for uncertain polytopic systems ensures that all closed-loop eigenvalues are lying in the defined LMI region. Two examples illustrate the effectiveness of the new design procedure.