By Cristobald de Kerchove, Paul Van Dooren (auth.), Rafael Bru, Sergio Romero-Vivó (eds.)
This quantity comprises the lawsuits of the "Third Multidisciplinary Symposium on confident platforms: thought and functions (POSTA09)" held in Valencia, Spain, September 2–4, 2009. at this time, this can be the one global congress whose major subject is concentrated in this box. After this 3rd occasion, the root of a standard triennial occasion supported within the activity of the former organizing committees has develop into established.
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Additional 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
Sample text
This fact represents a significant difference with respect to both standard switched systems and positive systems. Another significant fact, which makes switched positive systems different from the previous ones we considered, is that monomial reachability is no longer sufficient for reachability. This is rather intuitive as, indeed, nonnegative combinations of switching sequences do not generally lead to admissible switching sequences (as they do not take values in P). To explore monomial reachability and reachability, it is first convenient to provide the explicit expression of the state at any time instant k ∈ Æ, starting from the initial condition x(0), under the effect of the input sequence u(0), u(1), .
References 1. : Random Dynamical Systems. Springer, Heidelberg (1998) 2. : From attractor to chaotic saddle: a tale of transverse instability. Nonlinearity 9, 703–737 (1996) Lyapunov Exponents and Normal Repellers 27 3. : Lyapunov Exponents and the Mathematics of Invasion in Oscillatory or Chaotic Populations. Theor. Population Biol. 48, 126–171 (1995) 4. : Robust Permanence for Ecological Differential Equations, Minimax, and Discretizations. SIAM J. Math. Anal. 34, 1007–1039 (2003) 5. : Chain transitivity, attractivity and strong repellors for semidynamical systems.
For positive switched systems, instead, if a switching sequence σ of length k exists such that Cone (Rk (σ )) = Ên+ , then the Reachability Analysis for Different Classes of Positive Systems 39 system is reachable, but the converse is not true [27]. Even the weaker condition that there exists a finite number of switching sequences of finite lengths, such that the union of the cones generated by the columns of their reachability matrices covers the positive orthant, is only sufficient for the system reachability.