This paper presents a new approach dealing with the decentralized control of non linear interconnected systems. The key of this work is, on one hand, the description of the nonlinear systems using the Kronecker product notations which allow important manipulations, and on the other hand the use of the Lyapunov’s direct method of stability analysis, associated with a quadratic function. The prop...

‎In this paper‎, ‎we study stability of fractional-order nonlinear dynamic systems by means of Lyapunov‎ ‎method‎. ‎To examine the obtained results‎, ‎we employe the developed techniques on test examples‎.

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, the concept of command-tostate/output mapping is introduced for robust estimation under output feedback. Speci£cally, robust estimation is achieved if a command-to-state mapping of the plant converges to that of an uncertainty-free observer. It is shown using the Lyapunov direct method that, for a command-to-state mapping to be convergent, the Jacobian system corresponding to the...

Stability of linear systems with norm-bounded uncertainties and uncertain time-varying delays is considered. The delay is supposed to be bounded and fast varying (without any constraints on the delay derivative). Sufficient stability conditions are derived by direct Lyapunov method based on the complete Lyapunov–Krasovskii functional (LKF). A novel complete LKF construction is presented: the de...

We consider the computationally prohibitive problem of stability and invariance verification of large-scale dynamical systems. We exploit the natural interconnected structure often arising from such systems in practice (i.e., they are interconnections of low-dimensional subsystems), and propose a compositional method. We construct independently for each subsystem a Lyapunov-like function, and g...

We introduce the concept of a Lyapunov game as a subclass of strictly dominated games and potential games. The advantage of this approach is that every ergodic system (repeated game) can be represented by a Lyapunov-like function. A direct acyclic graph is associated with a game. The graph structure represents the dependencies existing between the strategy profiles. By definition, a Lyapunov-li...