TY - GEN
T1 - Controllability of Higher Order Linear Systems with Multiple Delays in Control
AU - Klamka, Jerzy
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - In the present chapter finite-dimensional dynamical control systems described by linear higher-order ordinary differential state equations with multiple point delays in control are considered. Using algebraic methods, necessary and sufficient conditions for relative controllability in a given time interval for linear dynamical system with multiple point delays in control are formulated and proved. This condition is generalization to relative controllability case some previous results concerning controllability of linear dynamical systems without multiple point delays in the control. Proof of the main result is based on necessary and sufficient controllability condition for linear systems without delays in control. Simple numerical example, which illustrates theoretical result is also given. Finally, some remarks and comments on the existing results for controllability of dynamical systems with delays in control are also presented.
AB - In the present chapter finite-dimensional dynamical control systems described by linear higher-order ordinary differential state equations with multiple point delays in control are considered. Using algebraic methods, necessary and sufficient conditions for relative controllability in a given time interval for linear dynamical system with multiple point delays in control are formulated and proved. This condition is generalization to relative controllability case some previous results concerning controllability of linear dynamical systems without multiple point delays in the control. Proof of the main result is based on necessary and sufficient controllability condition for linear systems without delays in control. Simple numerical example, which illustrates theoretical result is also given. Finally, some remarks and comments on the existing results for controllability of dynamical systems with delays in control are also presented.
KW - Controllability
KW - Higher order systems
KW - Linear systems
UR - https://www.scopus.com/pages/publications/85088211198
U2 - 10.1007/978-3-030-50936-1_94
DO - 10.1007/978-3-030-50936-1_94
M3 - Conference contribution
AN - SCOPUS:85088211198
SN - 9783030509354
T3 - Advances in Intelligent Systems and Computing
SP - 1132
EP - 1140
BT - Advanced, Contemporary Control - Proceedings of KKA 2020—The 20th Polish Control Conference, 2020
A2 - Bartoszewicz, Andrzej
A2 - Kabzinski, Jacek
A2 - Kacprzyk, Janusz
PB - Springer
T2 - 20th Polish Control Conference, PCC 2020
Y2 - 22 June 2020 through 24 June 2020
ER -