Pole Assignment With Improved Control Performance by Means of Periodic Feedback

This technical note is concerned with the pole placement of continuous-time linear time-invariant (LTI) systems by means of LQ suboptimal periodic feedback. It is well-known that there exist infinitely many generalized sampled-data hold functions (GSHF) for any controllable LTI system to place the m...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2010-01, Vol.55 (1), p.248-252
Main Authors: Lavaei, J., Sojoudi, S., Aghdam, A.G.
Format: Article
Language:English
Subjects:
Applied sciences
Computer science
control theory
systems
Control system analysis
Control system synthesis
Control systems
Control theory
Control theory. Systems
Economic models
Equivalence
Exact sciences and technology
Feedback
Generalized sampled-data hold functions (GSHF)
Java
Linear feedback control systems
Linear matrix inequalities
linear matrix inequality (LMI)
linear time-invariant (LTI)
linear time-varying (LTV)
Mathematical analysis
Mathematical models
Optimization
Performance analysis
Pole placement
Polynomials
Radar applications
Robots
State feedback
Studies
zero-order hold (ZOH)
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Summary:This technical note is concerned with the pole placement of continuous-time linear time-invariant (LTI) systems by means of LQ suboptimal periodic feedback. It is well-known that there exist infinitely many generalized sampled-data hold functions (GSHF) for any controllable LTI system to place the modes of its discrete-time equivalent model at prescribed locations. Among all such GSHFs, this technical note aims to find the one which also minimizes a given LQ performance index. To this end, the GSHF being sought is written as the sum of a particular GSHF and a homogeneous one. The particular GSHF can be readily obtained using the conventional pole-placement techniques. The homogeneous GSHF, on the other hand, is expressed as a linear combination of a finite number of functions such as polynomials, sinusoidals, etc. The problem of finding the optimal coefficients of this linear combination is then formulated as a linear matrix inequality (LMI) optimization. The procedure is illustrated by a numerical example.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2036295