Open-loop unstable feedback systems with double-sided inputs: An explicit demonstration of self-consistency: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

The standard formulation of linear shift-invariant feedback systems in the doubly infinite time axis setting lacks self-consistency with seemingly irreconcilable difficulties having been identified when the system is open-loop unstable. The available options for circumventing these difficulties for discrete-time SISO systems are highlighted and the manner in which they are exploited to obtain a self-consistent framework by reformulating the feedback systems in the space of distributions is clarified. In addition, it is explicitly demonstrated that causality and stability of a standard example are implied by the causality and stability of the equivalent system when reformulated in the self-consistent framework. © 2005 IEEE.