Design Degrees of Freedom in a Hybrid Observer for a Continuous Plant under an Intrinsic Pulse-modulated Feedback

Abstract

A hybrid observer for a linear time-invariant continuous plant under an intrinsic pulse-modulated feedback is considered. The fring times of the feedback representing the discrete state of the hybrid system to be observed are thus unknown. The observer possesses two feedback gains making use of the continuous output estimation error in order to correct the estimates of the continuous and discrete states, respectively. By driving the hybrid state estimation error to zero, the observer solves a synchronization problem between the fring times of the pulse-modulated feedback of the plant and that of the observer. Equivalence between a synchronous mode in the observer and zero output estimation error is proved. The influence of the observer design degrees of freedom on the observer performance is investigated by extensive numerical experiments. The introduction of the discrete observer gain clearly improves the observer performance for low-multiplicity periodic solutions in the plant but not for those with high multiplicity. In the latter case, suficiently fast observer convergence is achieved even for a zero value of the discrete gain.