Discrete-Time l ∞ and l2 Norm Vanishment and Low Gain Feedback with Their Applications in Constrained Control
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 l2 slow peaking phenomenon that exists in discrete-time systems under low gain feedback, more general notions of l∞ and l2 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 l2 slow peaking in the control input are respectively referred to as l∞ and l2 low gain feedback. Based on the notions of l∞ and l2 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 l2 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 l2 low gain feedback is instrumental in the control of discrete-time systems with control energy constraints. The notions of l∞ and l2-vanishment also result in a systematic approach to the design of l∞ and l2 low gain feedback by providing a family of solutions including those resulting from the existing design methods.
Slow peaking phenomenon l∞ and l2 norm vanishment l∞ and l2 low gain feedback constrained control.
Bin Zhou Zhao-Yan Li Zongli Lin
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P.O. Box 416, Har Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box
国际会议
The 24th Chinese Control and Decision Conference (第24届中国控制与决策学术年会 2012 CCDC)
太原
英文
2572-2577
2012-05-23（万方平台首次上网日期，不代表论文的发表时间）