<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Theodore E. Simos</style></author><author><style face="normal" font="default" size="100%">Vasilios N. Katsikis</style></author><author><style face="normal" font="default" size="100%">Spyridon D. Mourtas</style></author><author><style face="normal" font="default" size="100%">Predrag S. Stanimirović</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Unique non-negative definite solution of the time-varying algebraic Riccati equations with applications to stabilization of LTV systems</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics and Computers in Simulation</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Algebraic Riccati equations</style></keyword><keyword><style  face="normal" font="default" size="100%">Eigendecomposition</style></keyword><keyword><style  face="normal" font="default" size="100%">Linear time-varying systems</style></keyword><keyword><style  face="normal" font="default" size="100%">Zeroing neural network</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2022</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.sciencedirect.com/science/article/pii/S0378475422002452</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">202</style></volume><pages><style face="normal" font="default" size="100%">164-180</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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.</style></abstract></record></records></xml>