@article {SIMOS2022164,
	title = {Unique non-negative definite solution of the time-varying algebraic Riccati equations with applications to stabilization of LTV systems},
	journal = {Mathematics and Computers in Simulation},
	volume = {202},
	year = {2022},
	pages = {164-180},
	abstract = {In the context of infinite-horizon optimal control problems, the algebraic Riccati equations (ARE) arise when the stability of linear time-varying (LTV) systems is investigated. Using the zeroing neural network (ZNN) approach to solve the time-varying eigendecomposition-based ARE (TVE-ARE) problem, the ZNN model (ZNNTVE-ARE) for solving the TVE-ARE problem is introduced as a result of this research. Since the eigendecomposition approach is employed, the ZNNTVE-ARE model is designed to produce only the unique nonnegative definite solution of the time-varying ARE (TV-ARE) problem. It is worth mentioning that this model follows the principles of the ZNN method, which converges exponentially with time to a theoretical time-varying solution. The ZNNTVE-ARE model can also produce the eigenvector solution of the continuous-time Lyapunov equation (CLE) since the Lyapunov equation is a particular case of ARE. Moreover, this paper introduces a hybrid ZNN model for stabilizing LTV systems in which the ZNNTVE-ARE model is employed to solve the continuous-time ARE (CARE) related to the optimal control law. Experiments show that the ZNNTVE-ARE and HFTZNN-LTVSS models are both effective, and that the HFTZNN-LTVSS model always provides slightly better asymptotic stability than the models from which it is derived.},
	keywords = {Algebraic Riccati equations, Eigendecomposition, Linear time-varying systems, Zeroing neural network},
	issn = {0378-4754},
	doi = {https://doi.org/10.1016/j.matcom.2022.05.033},
	url = {https://www.sciencedirect.com/science/article/pii/S0378475422002452},
	author = {Theodore E. Simos and Vasilios N. Katsikis and Spyridon D. Mourtas and Predrag S. Stanimirovi{\'c}}
}
