Observer-based \(H_\infty\) controller for perturbed systems with state and input delays (Q1882411)

The objective of this paper is to present a new robust observer-based controller to stabilize a perturbed system with state and input delays. A sufficient condition for asymptotic stability is first derived. Then, based on this derivation, the observer-based \(H_{\infty}\) controller is structured not only to stabilize the closed-loop input-state delayed system, but also to reduce the \(H_{\infty}\) norm of the closed-loop transfer function from the disturbance to the controlled output. The proposed full-order observer-based \(H_{\infty}\) controller can be obtained by solving the proposed modified algebraic Riccati equations. Based on this derivation, the proposed observer-based robust controller not only reduces the influence of the disturbance, but also guarantees the closed-loop system stability. An example is given to illustrate the availability of the proposed design method.