Abstract
There are a few properties of the natural state space related to the memory of the input space. One of these is whether systems are determined by their natural state space; that is, the map from systems to natural state space is one to one. Systems represented by linear finite dimensional differential equations have this property, which may be desirable for understanding systems models in general. We present a counterexample. We give sufficient conditions such that systems are determined by their natural state space, which include tapered (memory) input spaces. We also present sufficient conditions for this property for systems represented by polynomial integral operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Root, W.L.: On the modeling of systems for identification. Part I: \(\varepsilon\)-representations of classes of systems. SIAM J. Control 13(4), 927–944 (1975)
Root, W.L.: Considerations regarding input and output spaces for time-varying systems. Appl. Math. Optim. 4, 365–384 (1978)
Root, W.L., Serakos, D.: The state of dynamical input–output systems as an operator. J. Math. Anal. Appl. 225, 224–248 (1998)
Serakos, D.: Topics in input–output systems theory: feedback systems with tapered input spaces, state and generalized adjoint systems. Ph.D. Dissertation, The University of Michigan (1988)
Serakos, D.: Some state space properties for a class of input–output systems. In: Proceedings of the 1994 Conference on Information Science and Systems, Department of Electrical Engineering, Princeton University, Princeton (1994)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Demetrios Serakos
About this chapter
Cite this chapter
Serakos, D. (2014). Some State Space Properties. In: State Space Consistency and Differentiability. SpringerBriefs in Optimization. Springer, Cham. https://doi.org/10.1007/978-3-319-14469-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-14469-6_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-14468-9
Online ISBN: 978-3-319-14469-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)