H_∞-state-feedback control of linear systems with small state delay

In this note, a H_∞ controller for systems with state delay is presented. For a prechosen γ the controller is obtained by solving Riccati partial differential inequalities (RPDIs). For small time delays, an asymptotic approximation of the controller is achieved by expanding the solution in powers of the delay. It is shown that a higher-order accuracy controller improves the performance. An example is brought where the results of the new method provide a satisfactory solution for a delay length comparable with the system 'bandwidth'. The performance of the system under the zero-order accuracy controller, which corresponds to systems without delay, is studied. Explicit formula for the guaranteed performance level is obtained for the delay lengths that preserve the internal stability of the system.