Exact-memory and memoryless control of linear systems with time-varying input delay using dynamic IQCs

Input delay is an important type of actuator nonlinearity in control systems. In this paper, we will address the output-feedback control synthesis problem for linear systems with time-varying input delay under the integral quadratic constraint (IQC) framework. A new exact-memory control scheme is first proposed, which consists of a standard linear output-feedback control law and an internal delay loop. The delay loop is embedded in the controller structure so as to reproduce the input delay behavior of the plant. By using quadratic Lyapunov functions incorporated with dynamic IQC multipliers, the resulting dynamic output-feedback delay control synthesis problem is fully characterized by a set of linear matrix inequalities (LMIs), which are convex on all design variables including the scaling factors associated with the IQC multipliers. Moreover, the corresponding result on memoryless control is also derived for the case when the plant input-delay information is not available for feedback control. An application to network systems has been used to illustrate the effectiveness and usefulness of the proposed approach.