In this technical note, a novel single-layer inverse-free fixed-time dynamical system (SIFDS) is proposed to address absolute value equations.
The proposed SIFDS directly employs coefficient matrix and absolute value equation function that aims at circumventing matrix inverse operation
and achieving fixed-time convergence. The equilibria of the proposed SIFDS is proved to be the unique solution of absolute value equation under
the mild condition. In contrast to most existing dynamical systems, the salient feature of the proposed SIFDS is its concise structure and tigh-
ter upper bound of convergence time. Moreover, theoretical analysis shows that our SIFDS possesses fixed-time convergence which is independent
of the initial values. To further improve the upper bound of convergence time of SIFDS, we establish a new global error bound for absolute value
equation. Finally, numerical simulation results are presented to validate the effectiveness of the proposed SIFDS.
Citation
X. Han, A new single-layer inverse-free fixed-time dynamical system for absolute value equations, [Online]. Available: https://optimization-online.org/wp-content/uploads/2023/06/IEAVEsonline620-1.pdf