The pseudorandom asymptotic behavior of digitally controlled analog systems

Summary form only given. The author has investigated some interesting descriptive and prescriptive questions that arise from a careful examination of the manner in which finite-precision phenomena, including measurement quantization and finite-wordlength arithmetic, affect the closed-loop performance of digitally controlled, discrete-time, state-space linear systems. In many cases of practical interest, a traditional signal-plus-noise analysis of these finite-precision effects is misleading at best. Nonetheless, recent work demonstrates that the asymptotic behavior of the systems considered is often best described in statistical terms; the time-evolution of such a system's state is usually chaotic, and its long-term macroscopic properties can often be summarized neatly in terms of a measure on the system's state space that is preserved by the closed-loop dynamics. The author is interested especially in understanding the ways in which various properties of this invariant measure (such as its differential entropy and ergodic decomposition) depend on the parameters of the open-loop system and on the choice of feedback control law.<
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