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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| Published in | IEEE transactions on automatic control Vol. 52; no. 5; pp. 767 - 781 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
IEEE
01.05.2007
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2007.895850 |
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| Abstract | 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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| AbstractList | 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. 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 |
| Author | Nesic, D. Liberzon, D. |
| Author_xml | – sequence: 1 givenname: D. surname: Liberzon fullname: Liberzon, D. organization: Coordinated Sci. Lab., Illinois Univ., Urbana, IL – sequence: 2 givenname: D. surname: Nesic fullname: Nesic, D. |
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| Keywords | 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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| SubjectTerms | 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 |
| Title | Input-to-State Stabilization of Linear Systems With Quantized State Measurements |
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