By Cristobald de Kerchove, Paul Van Dooren (auth.), Rafael Bru, Sergio Romero-Vivó (eds.)

This quantity includes the lawsuits of the "Third Multidisciplinary Symposium on optimistic structures: thought and purposes (POSTA09)" held in Valencia, Spain, September 2–4, 2009. at the present, this can be the single global congress whose major subject is concentrated in this box. After this 3rd occasion, the foundation of a customary triennial occasion supported within the activity of the former organizing committees has develop into established.

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Extra resources for Positive Systems: Proceedings of the third Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2009) Valencia, Spain, September 2-4, 2009

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95, 171–180 (1987) 10. : Monomial patterns in the sequence Ak b. Lin. Alg. Appl. 94, 89–101 (1987) 11. : Positive reachability and controllability of positive systems. Lin. Alg. Appl. 94, 35–53 (1987) 12. : Controllability of linear single-input positive discrete time systems. Int. J. of Control 50, 2523–2542 (1989) 13. : Controllability of multi-input positive discrete time systems. Int. J. of Control 51, 1295–1308 (1990) 14. : Positive linear systems: theory and applications. Series on Pure and Applied Mathematics.

Controllability of linear single-input positive discrete time systems. Int. J. of Control 50, 2523–2542 (1989) 13. : Controllability of multi-input positive discrete time systems. Int. J. of Control 51, 1295–1308 (1990) 14. : Positive linear systems: theory and applications. Series on Pure and Applied Mathematics. Wiley-Interscience, New York (2000) 15. : Doubly indexed dynamical systems. Math. Sys. Theory 12, 59–72 (1978) 16. : Global properties and duality in 2-D systems. Systems & Control Letters 2(1), 30–38 (1982) 17.

S It is easy to check that “=” is an equivalence relation on the set of monomial matrices. The following straightforward result will be needed below : Lemma 2. Let L and M be monomial matrices. Let P be a permutation matrix such that L = D1 P and M = P D2 where D1 and D2 are positive definite diagonal matrices. Then L and M are structuraly similar. Theorem 4. Consider a monomial system described by (1) and the quadratic cost (2) where C, R and S are diagonal matrices. Then the LQN closed-loop system is positive and therefore the solution of the LQN problem is solution of the LQN+ problem.

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