Positive Systems pp 331-338 | Cite as
Applications of Linear Co-positive Lyapunov Functions for Switched Linear Positive Systems
Conference paper
Abstract
In this paper we review necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for switched linear positive systems. Both the state dependent and arbitrary switching cases are considered and a number of applications are presented.
Keywords
Multiplicative Noise Positive System Positive Orthant Hurwitz Matrix Arbitrary Switching
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References
- 1.Arcak, M., Sontag, E.D.: Diagonal stability of a class of cyclic systems and its connection with the secant criterion. Automatica 42(9), 1531–1537 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
- 2.Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. In: Computer science and applied mathematics. Academic Press, New York (1979)Google Scholar
- 3.Farina, L., Rinaldi, S.: Positive Linear Systems. Wiley-Interscience Series. John Wiley & Sons, Inc., New York (2000)zbMATHGoogle Scholar
- 4.Foschini, G.J., Miljanic, Z.: A simple distributed autonomous power control algorithm and its convergence. IEEE Transactions on Vehicular Technology 42(4), 641–646 (1993)CrossRefGoogle Scholar
- 5.Gurvits, L., Shorten, R., Mason, O.: On the stability of switched positive linear systems. IEEE Transactions on Automatic Control 52(6), 1099–1103 (2007)CrossRefMathSciNetGoogle Scholar
- 6.Haddad, W.M., Chellaboina, V.: Stability theory for nonnegative and compartmental dynamical systems with time delay. Systems & Control Letters 51(5), 355–361 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
- 7.Hale, J., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. In: Applied Mathematical Sciences, vol. 99. Springer, New York (1993)Google Scholar
- 8.Hiriart-Urruty, J.B., Lemaréchal, C.: Fundamentals of convex analysis. Grundlehren Text Editions. Springer, Heidelberg (2001)zbMATHGoogle Scholar
- 9.Jacquez, J.A., Simon, C.P.: Qualitative theory of compartmental systems. SIAM Review 35(1), 43–79 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
- 10.Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control 48(6), 988–1001 (2003)CrossRefMathSciNetGoogle Scholar
- 11.Johnson, C.R.: Sufficient conditions for D-stability. Journal of Economic Theory 9(1), 53–62 (1974)CrossRefMathSciNetGoogle Scholar
- 12.Johnson, C.R., Mehrmann, V., Olesky, D.D.: Sign controllability of a nonnegative matrix and a positive vector. SIAM Journal on Matrix Analysis and Applications 14(2), 398–407 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
- 13.Kharitonov, V.L.: Robust stability analysis of time delay systems: A survey. Annual Reviews in Control 23, 185–196 (1999)Google Scholar
- 14.Knorn, F., Mason, O., Shorten, R.: On linear co-positive Lyapunov functions for sets of linear positive systems. Automatica (2008) (to appear)Google Scholar
- 15.Mason, O., Shorten, R.: On linear copositive Lyapunov functions and the stability of switched positive linear systems. IEEE Transactions on Automatic Control 52(7), 1346–1349 (2007)CrossRefMathSciNetGoogle Scholar
- 16.Meyn, S.P.: Control Techniques for Complex Networks. Cambridge University Press, New York (2008)zbMATHGoogle Scholar
- 17.Shorten, R., Wirth, F., Leith, D.J.: A positive systems model of tcp-like congestion control: asymptotic results. IEEE/ACM Transactions on Networking 14(3), 616–629 (2006)CrossRefMathSciNetGoogle Scholar
- 18.Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C.: Stability criteria for switched and hybrid systems. SIAM Review 49(4), 545–592 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
- 19.Song, Y., Gowda, M.S., Ravindran, G.: On some properties of P-matrix sets. Linear Algebra and its Applications 290(1-3), 237–246 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
- 20.Virnik, E.: Analysis of positive descriptor systems. Ph.D. thesis, Technische Universität Berlin, Germany (2008)Google Scholar
- 21.Šiljak, D.D.: Large-Scale Dynamic Systems: Stability and Structure. North-Holland Series in System Science and Engineering, vol. 3. North-Holland Publishing Co., New York (1979)Google Scholar
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