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SMALL-GAIN APPROACH to STABILITY ANALYSIS of HYBRID SYSTEMS

SMALL-GAIN APPROACH to STABILITY ANALYSIS of HYBRID SYSTEMS. Dragan Ne šić University of Melbourne, Australia. Daniel Liberzon Univ. of Illinois at Urbana-Champaign, USA. CDC ’05. HYBRID SYSTEMS as FEEDBACK CONNECTIONS. See CDC paper for more general setting.

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SMALL-GAIN APPROACH to STABILITY ANALYSIS of HYBRID SYSTEMS

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  1. SMALL-GAIN APPROACH to STABILITY ANALYSIS of HYBRID SYSTEMS Dragan Nešić University of Melbourne, Australia Daniel Liberzon Univ. of Illinois at Urbana-Champaign, USA CDC ’05

  2. HYBRID SYSTEMS as FEEDBACK CONNECTIONS See CDC paper for more general setting • Other decompositions possible • Can also have external signals continuous discrete

  3. SMALL–GAIN THEOREM • Input-to-state stability (ISS) from to [Sontag ’89]: • ISS from to : (small-gain condition) Small-gain theorem [Jiang-Teel-Praly ’94] gives GAS if:

  4. SUFFICIENT CONDITIONS for ISS • ISS from to if ISS-Lyapunov function [Sontag ’89]: • ISS from to if: and # of discrete events on is [Hespanha-L-Teel, TuC16.5]

  5. LYAPUNOV– BASED SMALL–GAIN THEOREM and # of discrete events on is Hybrid system is GAS if [L-Nešić, HSCC ’06]:

  6. SKETCH of PROOF [Jiang-Mareels-Wang ’96] is nonstrictly decreasing along trajectories Trajectories along which is constant? None! GAS follows by LaSalle for hybrid systems [Lygeros et al. ’03]

  7. APPLICATION: QUANTIZED CONTROL quantization error ISS from to with some linear gain Zoom in: where small-gain condition! ISS from to with gain External disturbances: [L-Nešić, ThC14.6]

  8. http://decision.csl.uiuc.edu/ liberzon CONCLUSIONS • Main idea: small-gain analysis tools are naturally • applicable to hybrid systems • Ongoing work: Lyapunov function constructions • for hybrid systems • Applications: • Quantized feedback control • Networked control systems [CDC paper, Nešić-Teel] • Other ???

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