LMI approach to H2 reduction model of switched systems

This paper presents the H2 model reduction problem for discrete-time switched systems using average dwell-time approach. First, by constructing multiple Lyapunov functions, the exponential stability criterion of switched systems under average dwell-time taualpha is established. Then, a reduced-order model for the underlying system is constructed, which guarantees these two models are close in H2 norm sense. Finally, an example is given to illustrate our results. All the results in this paper are expressed in terms of linear matrix inequalities (LMIs), which can be easily tested with efficient LMI algorithms.

[1]  Long Wang,et al.  Stabilization of switched linear systems with time-delay in detection of switching signal , 2005 .

[2]  G. Lastman.  Reduced-order aggregated models for bilinear time-invariant dynamical systems , 1984 .

[3]  K. Zhou.  Frequency-weighted L_∞ nomn and optimal Hankel norm model reduction , 1995 .

[4]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

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

[6]  James Lam,et al.  Model simplification for switched hybrid systems , 2006, Syst. Control. Lett..

[7]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[8]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[9]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[10]  Huijun Gao,et al.  H ∞ model reduction for discrete time-delay systems: delay-independent and dependent approaches , 2004 .

[11]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[12]  Kemin Zhou,et al.  Frequency-weighted 𝓛∞ norm and optimal Hankel norm model reduction , 1995, IEEE Trans. Autom. Control..

[13]  Long Wang,et al.  LMI approach to L/sub 2/-gain analysis and control synthesis of uncertain switched systems , 2004 .

[14]  James Lam,et al.  On H2 model reduction of bilinear systems , 2002, Autom..

[15]  Shaosheng Zhou,et al.  Generalized H2 output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions , 2006 .