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Positivity of continuous time irregular linear descriptor systems. (English) Zbl 1432.93125

Summary: The positivity of continuous-time irregular linear descriptor systems is investigated in this study. The present method is introduced based on Weierstrass decomposition. We obtain necessary and sufficient conditions for the positivity of the linear irregular descriptor systems. The conditions are investigated by two examples with Simulink/MATLAB.

MSC:

93C05 Linear systems in control theory
93C28 Positive control/observation systems
15B48 Positive matrices and their generalizations; cones of matrices

Software:

Simulink
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References:

[1] Berman A, Plemmons RJ. Nonnegative Matrices in the Mathematical Sciences. New York, NY, USA: Academic Press, 1979. · Zbl 0484.15016
[2] Bru R, Coll C, Romero-Vivo S, Sánchez E. Some problems about structural properties of positive descriptor systems. Lecture Notes in Control and Information Science 2003; 21: 233-240. · Zbl 1060.93065
[3] Chou JH, Chen SH, Zhang QL. Robust controllability for linear uncertain descriptor systems. Linear Algebra and Its Applications 2006; 414: 632-651. · Zbl 1152.93310
[4] Dai L. The difference between regularity and irregularity in singular systems. Circuits, Systems and Signal Processing 1989; 21: 435-444. · Zbl 0693.93034
[5] Duan GR. Analysis and Design of Descriptor Linear Systems. New York, NY, USA: Springer, 2010. · Zbl 1227.93001
[6] Farina L, Rinaldi S. Positive Linear Systems: Theory and Applications. 1st ed. New York, NY, USA: Wiley, 2000. · Zbl 0988.93002
[7] Gantmacher FR. Theory of Matrices. Vol. 2. New York, NY, USA: AMS Chelsea, 1960.
[8] Herrero A, Ramírez A, Thome N. Nonnegativity, stability, and regularization of discrete-time descriptor systems. Linear Algebra and Its Applications 2010; 432: 837-846. · Zbl 1181.93053
[9] Kaczorek T. Analysis of positivity and stability of discrete-time and continuous-time nonlinear systems. Computational Problems of Electrical Engineering 2015; 5: 11-16.
[10] Rami MA, Napp D. Characterization and stability of autonomous positive descriptor systems. IEEE Transactions on Automatic Control 2012; 21: 2668-2673. · Zbl 1369.93432
[11] Trazaska ZW. State-space descriptor models and asymptotic behavior of continuous-time positive control systems. Computers & Mathematics with Applications 1997; 34 (12): 1-10.
[12] Varga RS. Matrix Iterative Analysis. 2nd ed. New York, NY, USA: Springer, 2000. · Zbl 0998.65505
[13] Virnik E. Stability analysis of positive descriptor systems. Linear Algebra and Its Applications 2008; 21: 2640-2659. · Zbl 1147.93033
[14] Zhang G.
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