Equivalent description and stability analysis for discrete-time systems with uniformly distributed uncertainty

Abstract

We are concerned with discrete-time systems with uncertainty, which is assumed to be uniformly distributed over the unit interval [0,1]. To describe this uncertainty, the space {0,1}N, which is composed of all the infinite 0-1 sequences and endowed with the Haar measure, actually constitutes the underlying probability space. Therefore, it is shown that for stability analysis, such an uncertain system can be transformed into a switching system with switching sequences having maximal entropy. A stability criterion then is derived from this transformation. An illustrative example is included to show the effectiveness of the theoretical results.