Abstract
We study the behavior of discrete-time systems composed of a set of smooth transition maps coupled by a “quantized” feedback function. The feedback function partitions the state space into disjoint regions, and assigns a smooth transition function to each region. The main result is that under a constraint on the norm of the derivative of the transition maps, a bounded state trajectory with limit points in the interior of the switching regions leads to a region index sequence that is eventually periodic. Indeed, under these assumptions, we show that eventually the feedback function is determined by a finite state automaton. A similar result is proved in the case of finite state dynamic feedback.
Original language | English (US) |
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Pages (from-to) | 807-813 |
Number of pages | 7 |
Journal | IEEE Transactions on Automatic Control |
Volume | 35 |
Issue number | 7 |
DOIs | |
State | Published - Jan 1 1990 |
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering