QUANTIZATION and DELAY EFFECTS in NONLINEAR CONTROL SYSTEMS

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QUANTIZATION and DELAY EFFECTSin NONLINEAR
CONTROL SYSTEMS
Daniel Liberzon
Coordinated Science Laboratory and Dept. of
Electrical Computer Eng., Univ. of Illinois at
Urbana-Champaign
Notre Dame, Oct 18, 2005
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PROBLEM FORMULATION
Architecture-independent approach
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QUANTIZATION ONLY
Assume
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QUANTIZATION ONLY
quantization error
Assume
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QUANTIZATION and DELAY
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SMALL GAIN ARGUMENT
hence
ISS property becomes
Small gain
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FINAL RESULT
Need
small gain true
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FINAL RESULT
Need
small gain true
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FINAL RESULT
Need
small gain true
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FINAL RESULT
Need
small gain true
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FINAL RESULT
Need
small gain true
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VARIATIONS

• Relaxing ISS assumption

Previous approach works if is sufficiently
small

• Different system architecture

• External disturbances

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DYNAMIC QUANTIZATION
Can recover global asymptotic stability
Nesic-Liberzon 05