A Dilated LMI Approach to Continuous-Time Gain-Scheduled controller Synthesis with Parameter-Dependent Lyapunov Variables

Abstract This paper is concerned with the gain-scheduled controller synthesis for linear parameter varying (LPV) systems. In the case where the state space matrices of the system depend affinely on the time-varying parameters, the standard linear matrix inequalities (LMI’s) are helpful in dealing with such problems provided that we accept the notion of quadratic stability. However, in the case of rational parameter dependence, the standard LMI’s carry some deficiency and do not lead to numerically tractable conditions in a straightforward fashion. This paper clarifies that recently developed dilated LMI’s are effective in overcoming the difficulties and deriving numerically tractable conditions. The dilated LMI’s enable us also to employ parameter-dependent Lyapunov variables to achieve control objectives, which are known to be promising to alleviate the conservatism stemming from a quadratic (parameter-independent) Lyapunov variable.

[1]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[2]  Uri Shaked,et al.  Improved LMI representations for the analysis and the design of continuous-time systems with polytopic type uncertainty , 2001, IEEE Trans. Autom. Control..

[3]  P. Gahinet,et al.  A convex characterization of gain-scheduled H∞ controllers , 1995, IEEE Trans. Autom. Control..

[4]  Tetsuya Iwasaki,et al.  All controllers for the general H∞ control problem: LMI existence conditions and state space formulas , 1994, Autom..

[5]  Y. Ebihara,et al.  Robust controller synthesis with parameter-dependent Lyapunov variables: a dilated LMI approach , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  P. Gahinet,et al.  A linear matrix inequality approach to H∞ control , 1994 .

[7]  Robert E. Skelton,et al.  On stability tests for linear systems , 2002 .

[8]  Y. Ebihara,et al.  New dilated LMI characterizations for continuous-time control design and robust multiobjective control , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[9]  Karolos M. Grigoriadis,et al.  A unified algebraic approach to linear control design , 1998 .

[10]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[11]  Pierre Apkarian,et al.  Advanced gain-scheduling techniques for uncertain systems , 1998, IEEE Trans. Control. Syst. Technol..

[12]  Tomomichi Hagiwara,et al.  A dilated LMI approach to robust performance analysis of linear time-invariant uncertain systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[13]  J. Geromel,et al.  Extended H 2 and H norm characterizations and controller parametrizations for discrete-time systems , 2002 .

[14]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[15]  P. Gahinet,et al.  Affine parameter-dependent Lyapunov functions and real parametric uncertainty , 1996, IEEE Trans. Autom. Control..