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  1. Mathematics of Control, Signals, and Systems
  2. Mathematics of Control, Signals, and Systems : Volume 26
  3. Mathematics of Control, Signals, and Systems : Volume 26, Issue 4, December 2014
  4. Growth rates for persistently excited linear systems
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Mathematics of Control, Signals, and Systems : Volume 29
Mathematics of Control, Signals, and Systems : Volume 28
Mathematics of Control, Signals, and Systems : Volume 27
Mathematics of Control, Signals, and Systems : Volume 26
Mathematics of Control, Signals, and Systems : Volume 26, Issue 4, December 2014
Universal regular control for generic semilinear systems
Numerical schemes for nonlinear predictor feedback
How mild can slow controls be?
Stabilization of second-order evolution equations with time delay
Growth rates for persistently excited linear systems
Mathematics of Control, Signals, and Systems : Volume 26, Issue 3, September 2014
Mathematics of Control, Signals, and Systems : Volume 26, Issue 2, June 2014
Mathematics of Control, Signals, and Systems : Volume 26, Issue 1, March 2014
Mathematics of Control, Signals, and Systems : Volume 25
Mathematics of Control, Signals, and Systems : Volume 24
Mathematics of Control, Signals, and Systems : Volume 23
Mathematics of Control, Signals, and Systems : Volume 22
Mathematics of Control, Signals, and Systems : Volume 21
Mathematics of Control, Signals, and Systems : Volume 20
Mathematics of Control, Signals, and Systems : Volume 19
Mathematics of Control, Signals, and Systems : Volume 18
Mathematics of Control, Signals, and Systems : Volume 17
Mathematics of Control, Signals, and Systems : Volume 16
Mathematics of Control, Signals, and Systems : Volume 15
Mathematics of Control, Signals, and Systems : Volume 14
Mathematics of Control, Signals, and Systems : Volume 13
Mathematics of Control, Signals, and Systems : Volume 12
Mathematics of Control, Signals, and Systems : Volume 11
Mathematics of Control, Signals, and Systems : Volume 10

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Growth rates for persistently excited linear systems

Content Provider SpringerLink
Author Chitour, Yacine Colonius, Fritz Sigalotti, Mario
Copyright Year 2014
Abstract We consider a family of linear control systems $$\dot{x}=Ax+\alpha Bu$$ on $$\mathbb {R}^d$$ , where $$\alpha $$ belongs to a given class of persistently exciting signals. We seek maximal $$\alpha $$ -uniform stabilization and destabilization by means of linear feedbacks $$u=Kx$$ . We extend previous results obtained for bidimensional single-input linear control systems to the general case as follows: if there exists at least one $$K$$ such that the Lie algebra generated by $$A$$ and $$BK$$ is equal to the set of all $$d\times d$$ matrices, then the maximal rate of convergence of $$(A,B)$$ is equal to the maximal rate of divergence of $$(-A,-B)$$ . We also provide more precise results in the general single-input case, where the above result is obtained under the simpler assumption of controllability of the pair $$(A,B)$$ .
Starting Page 589
Ending Page 616
Page Count 28
File Format PDF
ISSN 09324194
Journal Mathematics of Control, Signals, and Systems
Volume Number 26
Issue Number 4
e-ISSN 1435568X
Language English
Publisher Springer London
Publisher Date 2014-04-08
Publisher Place London
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Time-varying systems Persistent excitation Uniform stabilization Maximal rate of exponential stability Lyapounov exponent Systems Theory, Control Control, Robotics, Mechatronics Communications Engineering, Networks
Content Type Text
Resource Type Article
Subject Control and Optimization Applied Mathematics Signal Processing Control and Systems Engineering
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