Dynamical behaviors in a recently proposed observer for linear time-invariant systems under intrinsic pulsemodulated feedback are studied. A special case of scalar continuous dynamics is considered as it is not covered by the previously presented mathematical analysis. Notably, the lowest non-trivial differential order of the continuous part of the plant results in a more complex dynamics of the observer. In fact, the convergence of the observer becomes dependent on the observer initialization,

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... which phenomenon does not exist in the case of the second and higher order continuous dynamics. As an alternative to the static gain observer, an integral feedback observer is suggested that exhibits global convergence for certain values of the observer gain and types of the periodic solution in the observed plant. Extensive bifurcation analysis is though necessary to select a proper observer gain. A. Churilov is with the polynomial of a matrix J m,n is P m,n (p) = p 2 − p tr J m,n + det J m,n . Schur stability of a polynomial P m,n (p) (all roots lie inside the unit circle) is then equivalent to | tr J m,n | − 1 < det J m,n < 1. By making use of the formulas for the partial derivatives given in Theorem 3 and checking inequalities (12), explicit stability conditions for the matrices J k,k+1 , J k−1,k+1 , J k,k , J k−1,k are obtained. Proposition 2: For k 1 we have The result follows from Theorem 3. For large gains K, i.e., K → +∞, Schur stability conditions for the polynomials P k,k+1 , P k−1,k+1 , P k,k , P k−1,k can be easily obtained. One has is satisfied, then the matrices J k−1,k , J k,k are Schur stable, i.e., all their eigenvalues lie strictly inside the unit circle. At the same time, tr J k−1,k+1 = tr J k,k+1 → +∞