1. The Complex Adaptive Delta-Modulator in Sliding Mode Theory
- Author
-
Dhafer Almakhles
- Subjects
Stability constraints ,0209 industrial biotechnology ,Delta modulator ,MathematicsofComputing_GENERAL ,General Physics and Astronomy ,lcsh:Astrophysics ,02 engineering and technology ,periodicity ,Stability (probability) ,Article ,single-bit ,020901 industrial engineering & automation ,two-level quantizer ,Control theory ,lcsh:QB460-466 ,0202 electrical engineering, electronic engineering, information engineering ,Data_FILES ,Sliding mode theory ,lcsh:Science ,Physics ,quasi-sliding mode ,020208 electrical & electronic engineering ,Hitting time ,Mode (statistics) ,adaptive delta-modulator ,Quasi sliding mode ,lcsh:QC1-999 ,Stability conditions ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,hitting-time ,Computer Science::Programming Languages ,lcsh:Q ,Software_PROGRAMMINGLANGUAGES ,lcsh:Physics - Abstract
In this paper, we consider the stability and various dynamical behaviors of both discrete-time delta modulator ( &Delta, M) and adaptive &Delta, M. The stability constraints and conditions of &Delta, M and adaptive &Delta, 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.
- Published
- 2020