A necessary and sufficient condition for robust H ∞ decentralized control via static output feedback

1999 ◽  
Vol 32 (2) ◽  
pp. 3137-3141
Author(s):  
Chen Bing ◽  
Wei Yongde ◽  
Zhang Siying
Keyword(s):  
Decentralized Control ◽  
Output Feedback ◽  
Sufficient Condition ◽  
Static Output Feedback ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Static Output

scholarly journals Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2158
Author(s):  
Vasilii Zaitsev ◽  
Inna Kim
Keyword(s):  
Output Feedback ◽  
Sufficient Conditions ◽  
The State ◽  
Distributed Delays ◽  
Static Output Feedback ◽  
Finite Spectrum ◽  
Multiple Variables ◽  
Linear Differential ◽  
Necessary And Sufficient ◽  
Static Output

We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results.

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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