TY - GEN
T1 - Discrete-time l ∞ and l 2 norm vanishment and low gain feedback with their applications in constrained control
AU - Zhou, Bin
AU - Li, Zhao Yan
AU - Lin, Zongli
PY - 2012
Y1 - 2012
N2 - The existing low gain feedback, which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero, has been designed in very specific ways. In this paper, by recognizing the l ∞ and l 2 slow peaking phenomenon that exists in discrete-time systems under low gain feedback, more general notions of l ∞ and l 2 norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals. Low gain feedback that does not lead to l ∞ and l 2 slow peaking in the control input are respectively referred to as l ∞ and l 2 low gain feedback. Based on the notions of l ∞ and l 2 vanishment, not only can the existing low gain feedback been recognized as an l ∞ low gain feedback, but also a new design approach referred to as the l 2 low gain feedback approach is developed for discrete-time linear systems. Parallel to the effectiveness of l ∞ low gain feedback in magnitude constrained control, the l 2 low gain feedback is instrumental in the control of discrete-time systems with control energy constraints. The notions of l ∞ and l 2-vanishment also result in a systematic approach to the design of l ∞ and l 2 low gain feedback by providing a family of solutions including those resulting from the existing design methods.
AB - The existing low gain feedback, which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero, has been designed in very specific ways. In this paper, by recognizing the l ∞ and l 2 slow peaking phenomenon that exists in discrete-time systems under low gain feedback, more general notions of l ∞ and l 2 norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals. Low gain feedback that does not lead to l ∞ and l 2 slow peaking in the control input are respectively referred to as l ∞ and l 2 low gain feedback. Based on the notions of l ∞ and l 2 vanishment, not only can the existing low gain feedback been recognized as an l ∞ low gain feedback, but also a new design approach referred to as the l 2 low gain feedback approach is developed for discrete-time linear systems. Parallel to the effectiveness of l ∞ low gain feedback in magnitude constrained control, the l 2 low gain feedback is instrumental in the control of discrete-time systems with control energy constraints. The notions of l ∞ and l 2-vanishment also result in a systematic approach to the design of l ∞ and l 2 low gain feedback by providing a family of solutions including those resulting from the existing design methods.
KW - Slow peaking phenomenon
KW - constrained control
KW - l and l low gain feedback
KW - l and l norm vanishment
UR - https://www.scopus.com/pages/publications/84866703579
U2 - 10.1109/CCDC.2012.6243053
DO - 10.1109/CCDC.2012.6243053
M3 - 会议稿件
AN - SCOPUS:84866703579
SN - 9781457720727
T3 - Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012
SP - 2560
EP - 2565
BT - Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012
T2 - 2012 24th Chinese Control and Decision Conference, CCDC 2012
Y2 - 23 May 2012 through 25 May 2012
ER -