Output feedback PD H∞ controller design for descriptor system

Proportional and derivative (PD) control has important significance in both theory and practical engineering. In this paper, we present a novel output feedback PD control problem for descriptor systems to guarantee both stability and disturbance attenuation. Sufficient and necessary solvability conditions are presented for the PD H_∞ control problem of descriptor systems in state space framework. Different from some recent works on PID control on conventional systems, LMI-based convex approaches are firstly presented to construct all of the dynamic output feedback PD H_∞ controllers and some confinements on plants can be removed. An example is provided to show the feasibility of our approach.