Brief paper: Strict linear matrix inequality characterisation of positive realness for linear discrete-time descriptor systems

Positive realness is an important concept in control theory. For linear discrete-time descriptor systems, the positive realness lemma involves non-strict linear matrix inequality (LMI) and may cause numerical problems in practice. Here, strict LMI characterisation for positive realness for linear discrete-time descriptor systems is established. The new characterisation can be efficiently solved by the standard LMI toolbox and may take important functions in related design problems.

[1]  S. Ding,et al.  Fault estimation and fault-tolerant control for descriptor systems via proportional, multiple-integral and derivative observer design , 2007 .

[2]  Ql Zhang,et al.  Robust impulse-eliminating control for descriptor systems , 2002 .

[3]  James Lam,et al.  LMI synthesis of H2 and mixed H2/H∞ controllers for singular systems , 2003, IEEE Trans. Circuits Syst. II Express Briefs.

[4]  L. Dai,et al.  Singular Control Systems , 1989, Lecture Notes in Control and Information Sciences.

[5]  Zidong Wang,et al.  Parametric circular eigenvalue assignment for descriptor systems via state feedback , 2000 .

[6]  Karl Johan Åström,et al.  Theory and applications of adaptive control - A survey , 1983, Autom..

[7]  Hai-Hua Yu,et al.  Robust pole assignment in high-order descriptor linear systems via proportional plus derivative state feedback , 2008 .

[8]  Qingling Zhang,et al.  Passivity and Optimal Control of Descriptor Biological Complex Systems , 2008, IEEE Transactions on Automatic Control.

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

[10]  Shengyuan Xu,et al.  On positive realness of descriptor systems , 2002 .

[11]  Guanghong Yang,et al.  Analysis on robust stability for interval descriptor systems , 2001 .

[12]  Yuanqing Xia,et al.  Control for discrete singular hybrid systems , 2008, Autom..

[13]  Delin Chu,et al.  The extended J-spectral factorization for descriptor systems , 2008, Autom..

[14]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .

[15]  Mohamed Darouach,et al.  Optimal unbiased reduced order filtering for discrete-time descriptor systems via LMI , 2009, Syst. Control. Lett..

[16]  Delin Chu,et al.  Algebraic Characterizations for Positive Realness of Descriptor Systems , 2008, SIAM J. Matrix Anal. Appl..

[17]  E. Jury,et al.  Discrete-time positive-real lemma revisited: the discrete-time counterpart of the Kalman-Yakubovitch lemma , 1994 .

[18]  Shengyuan Xu,et al.  Stabilization of discrete-time singular systems: a matrix inequalities approach , 1999, Autom..

[19]  B. Zhang,et al.  Parametric eigenstructure assignment by state feedback in descriptor systems , 2008 .

[20]  Yuanqing Xia,et al.  New bounded real lemma for discrete-time singular systems , 2008, Autom..

[21]  Yuanqing Xia,et al.  Stability and stabilization of continuous-time singular hybrid systems , 2009, Autom..

[22]  Chunyu Yang,et al.  Generalised absolute stability analysis and synthesis for Lur'e-type descriptor systems , 2007 .