SOS for Systems with Multiple Delays: Part 1. H∞-Optimal Control

We propose an LMI-based solution to the problem of H∞-optimal state-feedback control of systems with multiple state delays. This result is based on a generalization of the LMI framework to infinite-dimensional systems using the recently developed PQRS framework. The H∞ norm bounds are certified using Lyapunov-Krasovskii functionals and do not rely on discretization. The algorithms are scalable to large numbers of states and delays and accurate to at least 4 decimal places when compared with Pade-based methods. We include efficient implementations of the proposed controllers for realtime control and provide a user-friendly interface available online via Code Ocean.