A neutral system approach to H∞ PD/PI controller design of processes with uncertain input delay

• Time-delay processes with uncertain input delay are considered.
• Applying a PD controller to this process leads to a special system of neutral type.
• For stability analysis, a new Lyapunov–Krasovskii functional is presented.
• Sufficient conditions for the existence of H∞ PD/PI controller are derived.
• This method is applicable for a wide variety of process models.

This paper presents a neutral system approach to the design of an H∞ controller for input delay systems in presence of uncertain time-invariant delay. It is shown that when proportional derivative (PD) controller is applied to a time-delay system, the resulting closed loop system is generally a time-delay system of neutral type with delay term coefficients depending on the controller parameters. A descriptor model transformation is used to derive an advantageous bounded real lemma representation for the system. Furthermore, new delay-dependent sufficient conditions for the existence of an H∞ PD and PI controller in presence of uncertain delay are derived in terms of matrix inequalities. Some case studies and numerical examples are given in order to illustrate the advantages of the proposed method.