IEEE Control Systems Letters · 2020 · 45 citations · 14 references
EngineeringMathematicsSystems EngineeringDynamical SystemsSystems AnalysisSystems ModelingControl Of Dynamical SystemsControl SystemsControl TheoryDynamic Systems AnalysisNonlinear ControlSystem IdentificationControllabilityControllability AnalysisIdentifiability AnalysisIdentification Of Dynamical SystemsLinear System IdentificationLinear Time-invariant SystemsSingular Value DecompositionSystem Controllability
The fundamental lemma due to Willems et al. “A note on persistency of excitation,” Syst. Control Lett., vol. 54, no. 4, pp. 325-329, 2005 plays an important role in system identification and data-driven control. One of the assumptions for the fundamental lemma is that the underlying linear time-invariant system is controllable. In this letter, the fundamental lemma is extended to address system identification for uncontrollable systems. Then, a data-driven algebraic test is derived to check whether the underlying system is controllable or not. An algorithm based on the singular value decomposition of a Hankel matrix constructed from the data is provided to implement the developed test. The algorithm has cubic computational cost. Examples are given to illustrate the theoretical results.
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Adaptive filtering, prediction and control
Pétros Ioannou · Automatica · 1985 · 4.5K citations
A note on persistency of excitation
Jan C. Willems, Paolo Rapisarda, Ivan Markovsky et al. · Systems & Control Letters · 2004 · 1K citations