Design of reduced order H_∞ controllers

This paper presents a design method of H_∞ controllers with reduced order observers. For a plant with state of dimension n and measured output of dimension p, controllers with observers of order r≤(n-p) are designed by solving two Riccati equations of order n and r whose solutions should satisfy a coupling condition (spectral radius condition). Both Riccati equations are explicitly characterized so that they can be solved using standard techniques. The design methodology is presented for systems with noise-free measured output but can be directly extended to the case of noisy measured output.