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.

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 Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Mounir Hammouche ◽  
Philippe Lutz ◽  
Micky Rakotondrabe
Keyword(s):  
State Space ◽  
Output Feedback ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
State Space Model ◽  
Output Feedback Control ◽  
Optimal Solution ◽  
Loop System ◽  
Closed Loop System ◽  
Optimal Output

The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.

Output Feedback Assignability for Nonlinear Min-Max Systems

2011 ◽  
Vol 314-316 ◽  
pp. 374-379
Author(s):  
Hong Yun Wei ◽  
Zhong Xun Zhu ◽  
Yue Gang Tao ◽  
Wen De Chen
Keyword(s):  
Output Feedback ◽  
Cycle Time ◽  
Closed Loop ◽  
Loop System ◽  
Closed Loop System ◽  
Sufficient Criterion ◽  
Feedback Cycle ◽  
Necessary And Sufficient ◽  
Coloring Graph

This paper investigates the output feedback cycle time assignability of the min-max systems which are more complex than the systems studied in recent years. Max-plus projection representation for the closed-loop system with min-max output feedback is introduced. The coloring graph is presented and applied to analyze the structure of systems effectively. The necessary and sufficient criterion for the output feedback cycle time assignability is established which is an extension of the results studied before. The methods are constructive in nature.

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