A descriptor system approach to robust H_∞ control for linear systems with time-varying uncertainties

This article addresses the problems of robust H_∞ performance analysis and synthesis for continuous-time linear systems with time-varying uncertainties using parameter-dependent Lyapunov functions. An H_∞ performance criterion in terms of linear matrix inequalities is derived via employing a descriptor model transformation of linear systems with polytopic uncertainties (polytopic systems). This H_∞ performance criterion can be applied to robust controller synthesis and filtering design. The descriptor system approach is also taken to explore robust H_∞ performance analysis and controller synthesis of affine parameter systems. A flight control system and two numerical examples are given to illustrate the effectiveness of the proposed analysis and synthesis procedures.