Time and space complexity in feedback systems: Recent progress and challenges

It is a mandatory requirement that communication channels use signal sampling and quantization, which introduce errors. As a result, algorithms must be devised to recover or estimate the input signals to the channels. Signal estimation introduces dynamic delays and affect feedback systems´ stability and performance. Theoretically, sampling and quantization may be viewed as a means of reducing time and space complexity (TSC) of the data. A fundamental question is: How is TSC in data related to system stability and performance? Is there a fundamental limit on TSC for stability of feedback? This paper discusses signal estimation and their implications on stability and performance limitations of feedback systems with communication channels. Typical empirical measure based algorithms are modified with exponential weighting to accommodate time-varying natures of signal estimation problems. It is shown that such algorithms can be represented as an exponential averaging filter which affects feedback stability and performance. Recent advances and challenges in this direction are discussed.