Discrete-Time Dynamical Systems on Structured State Spaces: State-Transition Laws in Finite-Dimensional Lie Algebras
Year: 2025
Type: article
Abstract: The present paper elaborates on the development of a theory of discrete-time dynamical systems on finite-dimensional structured state spaces. Dynamical systems on structured state spaces possess well-known applications to solving differential equations in physics, and it was shown that discrete-time systems on finite- (albeit high-) dimensional structured state spaces possess solid applications to structured signal processing and nonlinear system identification, modeling and control. With reference to the state-space representation of dynamical systems, the present contribution tackles the core system-theoretic problem of determining suitable laws to express a system’s state transition. In particular, the present contribution aims at formulating a fairly general class of state-transition laws over the Lie algebra associated to a Lie group and at extending some properties of classical dynamical systems to process Lie-algebra-valued state signals.
Source: Symmetry
DOI: 10.3390/sym17030463
Author: Simone Fiori
Institution: Marche Polytechnic University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4408669954