Stability of Adaptive Delta Modulators with Constant Inputs

S.H. Dandach, S. Dasgupta (USA), and B.D.O. Anderson (Australia)


: Adaptive Delta Modulation, Convergence, Sta bility, Control, Limit Cycles


Motivated by applications to feedback control over com munication networks where the actuation and feedback signals are transmitted over communication channels, we study the stability of Adaptive Delta Modulators when the coded signal is a constant. The importance of such a set ting arises because a common control task is to track a dc input. We show that virtually all combinations of the algo rithm parameters result in 4-cycles, that the avoidance of 4 cycles requires a nongeneric initialization, and that steady state oscillations that generically arise can have amplitudes that can be arbitrarily close to the initial error.

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