Abstract
AbstractIn this paper various properties of discrete-time dynamic control systems trajectories with respect to state-space corner regions are considered. The known notion of state-space invariance serves as a basis for derivation of the whole family of dynamics behaviors for which both necessary and sufficient conditions are derived in a general nonlinear case as well as in the linear time-invariant case, shortly LTI-case. Specific examples are given for every case considered, and the proposed notions are analyzed with both theoretical and practical usefulness in mind. For the general nonlinear case a geometric approach is used, which provides a direct insight into the nature of trajectories’ behavior. In the LTI-case a geometric approach is used as well, but it is also translated into the purely algebraic set of conditions allowing for a direct analysis of system matrices. The presented family of control systems expands on the classical state-space invariance (and positive systems) analysis, thus potentially opening new research venues in this branch of control theory and system dynamics in general.
Publisher
Springer Science and Business Media LLC
Reference20 articles.
1. Bouligand, G.: Introduction à la Géométrie Infinitesimale Directe. Gauthiers-Villars, Paris Bourgin (1932)
2. Nagumo, M.: Über die Lage der Integralkurven gewönlicher Differentialglaichungen. Proc. Physico-Math. Soc. Jpn. 24(3), 551–559 (1942)
3. Aubin, J.-P.: Viability Theory. Birkhauser, Boston (1991)
4. Aubin, J.-P.: Dynamic Economic Theory: A Viability Approach. Springer, Berlin (1997)
5. Aubin, J.-P., Cellina, A.: Differential Inclusions. Springer, Berlin (1984)