TY - GEN

T1 - Stability of digitally interconnected linear systems

AU - Johnson, Taylor T.

AU - Mitra, Sayan

AU - Langbort, Cedric

PY - 2011/12/1

Y1 - 2011/12/1

N2 - A sufficient condition for stability of linear subsystems interconnected by digitized signals is presented. There is a digitizer for each linear subsystem that periodically samples an input signal and produces an output that is quantized and saturated. The output of the digitizer is then fed as an input (in the usual sense) to the linear subsystem. Due to digitization, each subsystem behaves as a switched affine system, where state-dependent switches are induced by the digitizer. For each quantization region, a storage function is computed for each subsystem by solving appropriate linear matrix inequalities (LMIs), and the sum of these storage functions is a Lyapunov function for the interconnected system. Finally, using a condition on the sampling period, we specify a subset of the unsaturated state space from which all executions of the interconnected system reach a neighborhood of the quantization region containing the origin. The sampling period proves to be pivotal-if it is too small, then a dwell-time argument cannot be used to establish convergence, while if it is too large, an unstable subsystem may not receive timely-enough inputs to avoid diverging.

AB - A sufficient condition for stability of linear subsystems interconnected by digitized signals is presented. There is a digitizer for each linear subsystem that periodically samples an input signal and produces an output that is quantized and saturated. The output of the digitizer is then fed as an input (in the usual sense) to the linear subsystem. Due to digitization, each subsystem behaves as a switched affine system, where state-dependent switches are induced by the digitizer. For each quantization region, a storage function is computed for each subsystem by solving appropriate linear matrix inequalities (LMIs), and the sum of these storage functions is a Lyapunov function for the interconnected system. Finally, using a condition on the sampling period, we specify a subset of the unsaturated state space from which all executions of the interconnected system reach a neighborhood of the quantization region containing the origin. The sampling period proves to be pivotal-if it is too small, then a dwell-time argument cannot be used to establish convergence, while if it is too large, an unstable subsystem may not receive timely-enough inputs to avoid diverging.

UR - http://www.scopus.com/inward/record.url?scp=84860692650&partnerID=8YFLogxK

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U2 - 10.1109/CDC.2011.6161264

DO - 10.1109/CDC.2011.6161264

M3 - Conference contribution

AN - SCOPUS:84860692650

SN - 9781612848006

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2687

EP - 2692

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Y2 - 12 December 2011 through 15 December 2011

ER -