Introduction to mathematical systems theory: a behavioral approach
Introduction to mathematical systems theory: a behavioral approach
Survey Invariant representations of discrete-time periodic systems
Automatica (Journal of IFAC)
Behavioral Systems Theory: A Survey
International Journal of Applied Mathematics and Computer Science - Selected Problems of Computer Science and Control
| Hi-index | 22.14 |
We consider periodic behavioral systems as introduced in [Kuijper, M., & Willems, J. C. (1997). A behavioral framework for periodically time-varying systems. In Proceedings of the 36th conference on decision & control (Vol. 3, pp. 2013-2016). San Diego, California, USA, 10-12 December 1997] and analyze two main issues: behavioral representation/controllability and autonomy. More concretely, we study the equivalence and the minimality of kernel representations, and introduce latent variable (and, in particular, image) representations. Moreover we relate the controllability of a periodic system with the controllability of an associated time-invariant system known as lifted system, and derive a controllability test. Further, we prove the existence of an autonomous/controllable decomposition similar to the time-invariant case. Finally, we introduce a new concept of free variables and inputs, which can be regarded as a generalization of the one adopted for time-invariant systems, but appears to be more adequate for the periodic case.