New approach to gain-scheduled H2 controller synthesis for continuous-time polytopic LPV systems

This paper is concerned with the problem of gain-scheduled H
₂
controller synthesis for continuous-time linear parameter-varying systems. By employing a basis-parameter dependent Lyapunov function and introducing some slack variables to the well-established performance conditions, sufficient conditions for the existence of the desired gain-scheduled H
₂
state feedback are established in terms of parameterized linear matrix inequalities. Based on the polytopic characteristic of the dependent parameters and a convexification method, the corresponding controller synthesis problem is then cast into finite-dimensional convex optimization problem which can be efficiently solved by using standard numerical softwares. A numerical example is given to illustrate the effectiveness and advantage of the proposed method.