STABILITY ANALYSIS of HYBRID SYSTEMS via SMALLGAIN THEOREMS

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STABILITY ANALYSIS of HYBRID SYSTEMS via
SMALL-GAIN THEOREMS
Daniel Liberzon Univ. of Illinois at
Urbana-Champaign, USA
Dragan Neic University of Melbourne, Australia
HSCC 06
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HYBRID SYSTEMS as FEEDBACK CONNECTIONS
continuous
discrete
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SMALL GAIN THEOREM
Small-gain theorem Jiang-Teel-Praly 94 gives
GAS if
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SUFFICIENT CONDITIONS for ISS
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LYAPUNOV BASED SMALL GAIN THEOREM
Hybrid system is GAS if
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SKETCH of PROOF
None!
GAS follows by LaSalle principle for hybrid
systems Lygeros et al. 03, Sanfelice-Goebel-Tee
l 05
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APPLICATION QUANTIZED CONTROL
Neic-L, CDC05
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CONCLUSIONS

• Main idea small-gain analysis tools are
  naturally
• applicable to hybrid systems

• Ongoing work Lyapunov function constructions
• for hybrid systems (more on this in the paper)

• Applications
• Quantized feedback control
• Networked control systems CDC paper,
  Neic-Teel
• Other ???