New math model fixes a decades-old problem in control systems
Researchers have solved a longstanding challenge in control theory: how to simplify complex systems without losing accuracy. The breakthrough could improve efficiency in robotics, manufacturing, and autonomous systems—anywhere precise control matters and computational power is limited.
Originaltitel: Minimal eventually positive realizations of externally positive systems
<p>It is a well-known fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. As a consequence, we show that in discrete-time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of Markov coefficients of the impulse response. In continuous-time, instead, if the sampling time is chosen sufficiently long, a minimal eventually positive realization leads always to a sampled realization which is minimal and positive.</p>