The trouble with imaginary eigenvalues. Optimal control, controllability, frequency response

2020/03/09 by Gharesifard, Bahman, Lewis, Andrew D.
#46F10 #47N70 #49N10 #93B52 #93C05 #93C80 #93D15 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2003.04374

Abstract

We investigate a few problems in the theory of linear time-invariant systems that arise when the open-loop system possesses imaginary eigenvalues. The problems are: (1) the infinite horizon, minimum energy optimal control problem; (2) the matter of defining the controllability Gramian for systems that are not stable; (3) the regularity as a distribution of the Fourier transform of the state impulse response. Apart from separately investigating these problems, we also indicate how they are interconnected.

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