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A2-2 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo...

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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) ( ) ( ) t t t + = + x Ax Bu (1) where ( ) , , and ( ) n n n n m m t t × × ∈ℜ ∈ℜ ∈ℜ ∈ℜ x A B u . In case the state vector ( ) t x is available and by using linear state feedback: ( ) ( ) t t = u Fx (2) the system (1) can be closed and we have: ( 1) ( ), =0, 1, 2... t t t + = c x A x (3) where c = + A A BF .
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