H∞ control of singularly perturbed systems with multiple delays

An infinite horizon H_∞ control problem for singularly perturbed linear systems with multiple point-wise and distributed small state delays is considered. This problem is solved by its asymptotic slow-fast decomposition yielding two much simpler parameter-free H_∞ control problems, the slow and fast ones. Each of these two problems is solved by the Riccati Matrix Inequality/Equation method. A solution (control) of the original problem is obtained as some composition of solutions of the slow and fast problems. Gain matrices of the obtained control are parameter-free, and it solves the original problem for all sufficiently small values of the parameter of singular perturbations. An illustrative example is presented.