Normalized coprime representations for time-varying linear systems
Institute of Electrical and Electronics Engineers (IEEE)
By considering the behaviour of stabilizable and detectable, linear time-varying state-space models over doublyinfinite continuous time, we establish the existence of so-called normalized coprime representations for the system graphs; that is, stable and stably left (resp. right) invertible, image (resp. kernel) representations that are normalized with respect to the inner product on L²(−∞,∞); this is consistent with the notion of normalization used in the time-invariant setting. The approach is constructive, involving the solution of timevarying differential Riccati equations with single-point boundary conditions at either +∞ or −∞. The contribution lies in accommodating state-space models that may not define an exponential dichotomy.
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49th IEEE Conference on Decision and Control, Atlanta, USA, 15-17 December 2010
Proceedings of the 49th IEEE Conference on Decision and Control, pp. 7718 - 7723