Controller synthesis for robust performance using H∞ with transients for structured uncertainty

This paper considers the design of controllers to achieve, for a bounded class of systems, a specified balance between optimal infinite horizon disturbance rejection performance and regulation of transient behaviour caused by non-zero initial conditions. It represents an extension of the ´H_∞ with transients´ technique to permit structured uncertainty entering both the state and measurement equations. The existence of a controller is determined by the existence of a scaling matrix which admits solutions to both a scaled algebraic Riccati equation and scaled Riccati differential equation. Explicit formulae for a controller which achieves the robust performance are given. An insightful analysis of the worst case exogenous process disturbance/measurement noise and uncertainty input signals is given.