In this paper a parametric optimization problem for a linear neutral system with two delays with an integral quadratic performance index is formulated and solved. The method of computing of a performance index value bases on determining of a Lyapunov functional defined on a state space such that its value for an initial state is equal to a performance index value. In the paper a form of a Lyapu...

Using the integrability of sinh-Gordon equation, we demonstrate spectral stability its elliptic solutions. By constructing a Lyapunov functional using higher-order conserved quantities show that these solutions are orbitally stable with respect to subharmonic perturbations arbitrary period.

The paper shows that the global exponential stability property is preserved, under suitably fast sampling and small input-delay, whenever the dynamics of the time-delay system at hand and the related stabilizing (in continuous-time) state feedback are described by globally Lipschitz maps. The Halanay’s inequality is used in order to prove this result. Continuous-time, possibly non-affine in the...

In this article, an observer with delay-dependent stability conditions has been presented for time delay systems with unknown inputs, where the time delay terms exist in the state and output of the system. The designing of this observer, whose performance index is the H2 norm, has been formulated as a nonlinear optimization problem. By using the finite characterization of a Lyapunov functional ...

Periodic travelling waves are considered in the class of reduced Ostrovsky equations that describe low-frequency internal waves in the presence of rotation. The reduced Ostrovsky equations with either quadratic or cubic nonlinearities can be transformed to integrable equations of the Klein–Gordon type by means of a change of coordinates. By using the conserved momentum and energy as well as an ...

Abstract In this paper, we investigate the decay properties of thermoelastic suspension bridges model. We prove that energy is decaying exponentially. To our knowledge, result new and method proof based on to build appropriate Lyapunov functional.

in this paper a comprehensive approach is presented to improve power swings damping based on direct lyapunov method. the approach combines superconducting magnetic energy storage (smes) system with static synchronous compensator (statcom). considering the energy absorption/injection ability of smes, in transient states the combination exchanges both active and reactive powers with power system....

In this paper, we investigate the delay-dependent robust stability of fuzzy Cohen-Grossberg neural networks with Markovian jumping parameter and mixed time varying delays by delay decomposition method. A new Lyapunov-Krasovskii functional (LKF) is constructed by nonuniformly dividing discrete delay interval into multiple subinterval, and choosing proper functionals with different weighting matr...

In this paper, we investigate the partial practical exponential stability of neutral stochastic functional differential equations with Markovian switching. The main tool used to prove results is Lyapunov method. We analyze an illustrative example show applicability and interest results.

This paper is concerned with the problem of exponential stability for a class of stochastic neural networks with Markovian switching and mode-dependent interval time-varying delays. A novel Lyapunov-Krasovskii functional is introduced with the idea of delay-partitioning, and a new exponential stability criterion is derived based on the new functional and free-weighting matrix method. This new c...