Input-to-State Stabilization of Linear Systems With Quantized State Measurements

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Buildi...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 52; no. 5; pp. 767 - 781
Main Authors Liberzon, D., Nesic, D.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.05.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Adjustable
Applied sciences
Communication system control
Communication system security
Computer science; control theory; systems
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Disturbances
Dynamical systems
Dynamics
Exact sciences and technology
Feedback control
hybrid control
input-to-state stability (ISS)
International Space Station
Linear systems
Lyapunov method
quantized feedback
Robustness
Sampling methods
Stability
Strategy
Zooming
dynamic control
Hybrid control
Control synthesis
Continuous time
Dynamical system
Cascade systems
Linear control
Closed feedback
Input to state stability
input-to-state stability (ISS)
Quantized signal
Disturbances
Zoom
Quantifier
quantized feedback
Sampling
Lyapunov function
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ISSN0018-9286
1558-2523
DOI10.1109/TAC.2007.895850

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Summary:We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.895850