The Complex Adaptive Delta-Modulator in Sliding Mode Theory

In this paper, we consider the stability and various dynamical behaviors of both discrete-time delta modulator ([Formula: see text]-M) and adaptive [Formula: see text]-M. The stability constraints and conditions of [Formula: see text]-M and adaptive [Formula: see text]-M are derived following the theory of quasi-sliding mode. Furthermore, the periodic behaviors are explored for both the systems with steady-state inputs and certain parameter values. The results derived in this paper are validated using simulated examples which confirms the derived stability conditions and the existence of periodicity.