Parametric Lyapunov function approach to <i>H</i> ₂ analysis and control of linear parameter-dependent systems

Abstract

The problems of H2 analysis and control synthesis for linear continuous-time parameter-dependent systems are addressed. The admissible values of the parameters and their rates of variation are assumed to belong to a given polytope. Linear matrix inequality-based methods of H2 performance analysis and state feedback control are developed. Both the design of gain-scheduled and robust controllers are addressed. The proposed methods have the feature that stability as well as the guaranteed H2 performance cost are based on a parameter-dependent Lyapunov function which is quadratic on the system parameters. The controller implementation does not require online knowledge of the rate of variation of the parameters.