Stability Robustness of a Feedback Interconnection of Systems With Negative Imaginary Frequency Response

A necessary and sufficient condition, expressed simply as the dc loop gain (i.e., the loop gain at zero frequency) being less than unity, is given in this note to guarantee the internal stability of a feedback interconnection of linear time-invariant (LTI) multiple-input multiple-output systems with...

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Veröffentlicht in:IEEE transactions on automatic control Jg. 53; H. 4; S. 1042 - 1046
Hauptverfasser: Lanzon, A., Petersen, I.R.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.05.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Actuators
Applied sciences
Bounded-real systems
Computer science; control theory; systems
Control systems
Control theory
Control theory. Systems
Exact sciences and technology
Feedback
Feedback loop
Force sensors
Frequency response
Gain
Image sensors
Interconnection
MIMO
Negative feedback
passivity
positive position feedback
positive-real systems
Robust stability
Sensors
small-gain theorem
Stability
Studies
Sufficient conditions
System theory
Theorems
Transfer functions
MIMO system
Necessary and sufficient condition
small-gain theorem
Feedback regulation
Bounded-real systems
State space method
Passive system
Positive position feedback filter
Positive system
Passivity
positive position feedback
Linear time invariant system
Transducer position
Small gain theorem
Position sensor
Position measurement
positive-real systems
Robustness
Frequency response
Transfer function
Force control
ISSN:0018-9286, 1558-2523
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Beschreibung
Zusammenfassung:A necessary and sufficient condition, expressed simply as the dc loop gain (i.e., the loop gain at zero frequency) being less than unity, is given in this note to guarantee the internal stability of a feedback interconnection of linear time-invariant (LTI) multiple-input multiple-output systems with negative imaginary frequency response. Systems with negative imaginary frequency response arise, for example, when considering transfer functions from force actuators to colocated position sensors, and are commonly important in, for example, lightly damped structures. The key result presented here has similar application to the small-gain theorem, which refers to the stability of feedback interconnections of contractive gain systems, and the passivity theorem, which refers to the stability of feedback interconnections of positive real (or passive) systems. A complete state-space characterization of systems with negative imaginary frequency response is also given in this note and also an example that demonstrates the application of the key result is provided.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2008.919567