Stabilisation of the complex double integrator by means of a saturated linear feedback

2021/04/13 by Yacine Chitour, Chitour, Yacine
Mathematics · #34D23 #93D05 #93D15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Optimization and Control (math.OC) #math.CA #math.OC #msc:34D23 #msc:93D05 #msc:93D15

paper · pdf · doi:10.48550/arxiv.2104.06302

arxiv created 2021/04/13 · arxiv updated 2021/04/14

Abstract

Consider the saturated complex double integrator, i.e., the linear control system x=Ax+Bσ(u), where x∈\R⁴, u∈\R, B∈\R⁴, the 4× 4 matrix A is not diagolizable and admits a non zero purely imaginary eigenvalue of multiplicity two, the pair (A,B) is controllable and σ:\R→\R is a saturation function. We prove that there exists a linear feedback u=K^Tx such that the resulting closed loop system given by x=Ax+Bσ(K^Tx) is globally asymptotically stable with respect to the origin.

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