Spectrum Assignment and Stabilization by Static Output Feedback of Linear Difference Equations with State Variable Delays

2021 ◽  
Author(s):  
Adam Czornik ◽  
Michał Niezabitowski ◽  
Vasilii Zaitsev ◽  
Inna Kim
Keyword(s):  
Difference Equations ◽  
Output Feedback ◽  
Static Output Feedback ◽  
Linear Difference Equations ◽  
Spectrum Assignment ◽  
State Variable ◽  
Variable Delays ◽  
Static Output

scholarly journals Finite spectrum assignment in linear systems with several lumped and distributed delays by means of static output feedback

2020 ◽  
Vol 30 (3) ◽  
pp. 367-384
Author(s):  
I.G. Kim
Keyword(s):  
Output Feedback ◽  
Assignment Problem ◽  
Closed Loop ◽  
Loop System ◽  
Distributed Delays ◽  
Static Output Feedback ◽  
Closed Loop System ◽  
Finite Spectrum ◽  
Spectrum Assignment ◽  
Static Output

We consider a control system defined by a linear time-invariant system of differential equations with lumped and distributed delays in the state variable. We construct a controller for the system as linear static output feedback with lumped and distributed delays in the same nodes. We study a finite spectrum assignment problem for the closed-loop system. One needs to construct gain coefficients such that the characteristic function of the closed-loop system becomes a polynomial with arbitrary preassigned coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of the finite spectrum assignment problem. Corollaries on stabilization by linear static output feedback with several delays are obtained for the closed-loop system.

scholarly journals Spectrum assignment in linear systems with several commensurate lumped and distributed delays in state by means of static output feedback

2020 ◽  
Vol 56 ◽  
pp. 5-19
Author(s):  
V.A. Zaitsev ◽  
I.G. Kim
Keyword(s):  
Output Feedback ◽  
Assignment Problem ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Static Output Feedback ◽  
Spectrum Assignment ◽  
System A ◽  
Necessary And Sufficient ◽  
Derivatives Of ◽  
Static Output

A linear control system defined by a stationary differential equation of nth order with several commensurate lumped and distributed delays in state is considered. In the system, the input is a linear combination of m variables and their derivatives of order not more than n−p and the output is a k-dimensional vector of linear combinations of the state and its derivatives of order not more than p−1. For this system, a spectrum assignment problem by linear static output feedback with commensurate lumped and distributed delays is studied. Necessary and sufficient conditions are obtained for solvability of the arbitrary spectrum assignment problem by static output feedback controller. Corollaries on stabilization of the system are obtained.

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