Time Delay Control (TDC) for linear and nonlinear systems  
with uncertain dynamics has been widely discussed in the literature,  
as it has a very simple and compact form. It uses time-delayed  
signals for estimating unknown dynamics at an instant, and uses  
feedback linearization for cancellation of known and estimated  
unknown dynamics. Its implementation is more natural in digital  
form, though much analysis has been focused on the continuous  
version of the controller. This paper extends the recently  
improved sufficient stability conditions for Bounded Input-Bounded Output (BIBO) stability of continuous Time Delay  
Control to discrete Time Delay Control, including simplified  
approximate conditions under various assumptions. These  
results are intended to be practical, applicable to multi-input,  
multi-output nonlinear, time-varying systems, that are not necessarily  
affine in input, and for Time Delay or sampling time, (L)  
that is finite, but not necessarily infinitesimally small. This paper  
contrasts the derived conditions to earlier results for continuous  
Time Delay Control. In addition to the precise sufficient conditions, approximate conditions are derived under various assumptions of small sampling time, and/or ignoring plant dynamics for cases they are relatively slow. A design procedure is outlined using various conditions. Examples are used to illustrate the use of the various stability conditions and compared them to the actual conditions from simulations, as well as to the continuous TDC case. 


New Stability Analysis and Design of Discrete Time Delay Control for Nonaffine Nonlinear Systems

Division / Sponsors: 
Dynamic Systems & Control (DSCD)

Paper Proceedings: https://asmedigitalcollection.asme.org/DSCC/DSCC2020/volume/84270

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