Reconciliation of inconsistencies in the theory of linear systems

Ragnoli, E. and Leithead, W.E.; (2005) Reconciliation of inconsistencies in the theory of linear systems. In: Switching and Learning in Feedback Systems. Lecture Notes in Computer Science . Springer-Verlag, pp. 273-289. ISBN 978-3-540-24457-8 (http://dx.doi.org/10.1007/b105497)

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Abstract

In the last few years some articles have emphasized certain fundamental inconsistencies underlying feedback control theory. The paper of Willems [1] Georgiou and Smith [2], later the works of Makila [3],[4], of Leithead et al. [5] have stressed the inconsistency of standard formalisms of linear time-invariant systems when the signals are double sided and the systems are open loop unstable. We establish a framework for a consistent time domain and frequency domain representation of discrete time linear time-invariant systems and, furthermore, that supports the consistent analysis of discrete time linear time-invariant feedback systems when signals are double sided and the systems are open loop unstable.

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