Reconciliation of Inconsistencies in the Theory of Linear Systems

Abstract

AbstractIn 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.KeywordsLinear SpaceOpen LoopInverse Fourier TransformFrequency Response FunctionFrequency Domain AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.