# A2-2 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo ETAI'2005 Seventh National Conference with International Participation ETAI'2005 Ohrid

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POSITIVE EQUILIBRIUM OF LINEAR DISCRETE TIME SYSTEMS BY USING LINEAR STATE FEEDBACK S. Kostova 1 1 Institute of Control and System Research, Bulgarian Academy of Sciences, P.O.B. 79, 1113, Sofia, Bulgaria, Tel: +359 (2) 979 20 54 Fax: +359 (2) 8703 361 E-mail: [email protected] Abstract – Problem of interest in the paper is for a given discrete-time linear system, find, if possible, linear state-feedback control low such that the system have positive equilibrium point. Keywords – positive equilibrium, linear discrete time systems, linear state feedback. 1. INTRODUCTION, PRELIMINARIES AND PROBLEM DEFINITION Problem of interest in the paper is for a given discrete-time linear system, find, if possible, linear state-feedback control low such that the system have positive equilibrium point. We will call this problem positive equilibrium problem by linear state feedback. Consider linear discrete-time system: (1 ) ( ) ( ) tt t += + xA x B u (1) where () , , and () nn n n m m ×× ∈ℜ xAB u . In case the state vector () t x is available and by using linear state feedback: = uF x (2) the system (1) can be closed and we have: ( 1) ( ), =0, 1, 2. .. t c x (3) where c =+ AA B F .

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## This note was uploaded on 02/18/2010 for the course ITK ETF113L07 taught by Professor Popovskiborislav during the Spring '10 term at Pacific.

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A2-2 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo ETAI'2005 Seventh National Conference with International Participation ETAI'2005 Ohrid

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