TY - GEN

T1 - Finite gain stabilization with logarithmic quantization

AU - Zhang, Chun

AU - Dullerud, Geir E.

PY - 2007/12/1

Y1 - 2007/12/1

N2 - In this paper, we consider the finite-gain stabilization problem in the case where there is logarithmic quantization in the feedback loop; more specifically, we consider a scalar-input discrete-time linear time invariant (LTI) system in the presence of additive deterministic or stochastic external disturbances, with logarithmically quantized state measurements available. Assuming that finite ℓp gain from the input to the states is achievable when the feedback is not quantized (or in the stochastic case that the pth-moment is finite), we show that there exist feasible logarithmic quantizers such that these boundedness properties are preserved when the state feedback is quantized. The main contribution of this paper is to show that static memoryless logarithmic quantizer is sufficient for finite gain stabilization. The quantizer density only depends on the open-loop system parameters. In addition to the controller construction, we also give explicit bounds on the ℓp gain, and in the stochastic case, the p th-moment of the state.

AB - In this paper, we consider the finite-gain stabilization problem in the case where there is logarithmic quantization in the feedback loop; more specifically, we consider a scalar-input discrete-time linear time invariant (LTI) system in the presence of additive deterministic or stochastic external disturbances, with logarithmically quantized state measurements available. Assuming that finite ℓp gain from the input to the states is achievable when the feedback is not quantized (or in the stochastic case that the pth-moment is finite), we show that there exist feasible logarithmic quantizers such that these boundedness properties are preserved when the state feedback is quantized. The main contribution of this paper is to show that static memoryless logarithmic quantizer is sufficient for finite gain stabilization. The quantizer density only depends on the open-loop system parameters. In addition to the controller construction, we also give explicit bounds on the ℓp gain, and in the stochastic case, the p th-moment of the state.

UR - http://www.scopus.com/inward/record.url?scp=62749109668&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62749109668&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4434983

DO - 10.1109/CDC.2007.4434983

M3 - Conference contribution

AN - SCOPUS:62749109668

SN - 1424414989

SN - 9781424414987

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3952

EP - 3957

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

T2 - 46th IEEE Conference on Decision and Control 2007, CDC

Y2 - 12 December 2007 through 14 December 2007

ER -