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Keywords:

  • switched nonlinear system;
  • large-time observability;
  • high-gain observer;
  • hybrid-type observer;
  • uniform observability

SUMMARY

This paper presents a sufficient condition for observability of continuous-time switched nonlinear systems that also involve state jumps. Without the assumption of observability of individual modes, the sufficient condition is based on gathering partial information from each mode so that the state is completely recovered after several switchings. Based on the sufficient condition, a hybrid-type observer is designed, which comprises a copy of the actual plant and an error correction scheme at discrete time instants. In order to execute the proposed design, the observable component of the state at each mode needs to be estimated without transients or ‘peaking’ (caused by high-gain observers), and this motivates us to introduce a back-and-forth estimation technique. Under the assumption of persistent switching, analysis shows that the estimate thus generated converges asymptotically to the actual state of the system. Simulation results validate the utility of the proposed algorithm. Copyright © 2012 John Wiley & Sons, Ltd.