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On stabilization of linear systems with limited information

Abstract—We consider the problem of stabilizing a linear time-invariant system using sampled encoded measurements of its state or output. We derive a relationship between the number of values taken by the encoder and the norm of the transition matrix of t

OnStabilizationofLinearSystemsWith

LimitedInformation

DanielLiberzon

Abstract—Weconsidertheproblemofstabilizingalineartime-invariantsystemusingsampledencodedmeasurementsofitsstateoroutput.Wede-rivearelationshipbetweenthenumberofvaluestakenbytheencoderandthenormofthetransitionmatrixoftheopen-loopsystemoveronesam-plingperiod,whichguaranteesthatglobalasymptoticstabilizationcanbeachieved.Acodingschemeandastabilizingcontrolstrategyaredescribedexplicitly.

IndexTerms—Asymptoticstabilization,coding,limitedinformation,linearsystem,sampling.

I.INTRODUCTION

Supposethatwearegivenastabilizablelineartime-invariantsystem

x_=Ax+Bu;

x

On stabilization of linear systems with limited information

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