Stability plays an important role in the theory of dynamical systems and control. It characterizes the property of an unperturbed trajectory that all perturbed trajectories starting nearby stay nearby: small perturbations cause only small changes in the system behavior. The most important concept of stability has bee introduced by the Russian mathematician A. M. Lyapunov in 1892. Based on his f...

The stability of learning rate in neural network identifiers and controllers is one of the challenging issues which attracts great interest from researchers of neural networks. This paper suggests adaptive gradient descent algorithm with stable learning laws for modified dynamic neural network (MDNN) and studies the stability of this algorithm. Also, stable learning algorithm for parameters of ...

In this paper we present partial stability results; that is, stability with respect to part of the system's state, for nonlinear dynamical systems. Using these results we provide a rigorous uni cation between partial stability theory for autonomous systems and stability theory for nonlinear time-varying systems. This uni cation allows for time-varying stability theory to be presented as a speci...

The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering our understanding of matching market performance. We propose absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts other matchings when ...

The whole class of minimally coupled and massive scalar fields which may be responsible for flattening of galactic rotation curves is found. An interesting relation with a class of scalar-tensor theories able to isotropise anisotropic models of Universe is shown. The resulting metric is found and its stability and scalar field properties are tested with respect to the presence of a second scala...

we study the history and recent developments in nonelementarymodel theory focusing on the framework of abstractelementary classes. we discuss the role of syntax and semanticsand the motivation to generalize first order model theory to nonelementaryframeworks and illuminate the study with concrete examplesof classes of models. this first part introduces the main conceps and philosophies anddiscu...

We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the complexity of finding stable outcomes in such games, for several notions of stability. In particular, we provide an efficient algorithm that finds an individually st...