We perform a Lyapunov stability analysis of a special class of 2-D systems, those for which one of the independent variables plays a distinguished role. We show how to construct Lyapunov functionals for this class using LMIs. We also apply our results to the study of quarter-plane stability. © 2012 Elsevier Ltd. All rights reserved.

The known concepts of Lyapunov exponent, moment Lyapunov exponents, and stability index for stationary points of stochastic systems are carried over for invariant orbits with nonvanishing di usion. The obtained general results are applied to investigating stochastic stability and stabilization of orbits on the plane.

In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special ei...

In this paper we introduce a generalized class of filtered Lyapunov functions, which are Lyapunov functions with time-varying parameters satisfying certain differential equations. Filtered Lyapunov functions have the same stability and robustness properties of Lyapunov functions. On the other hand, filtered Lyapunov functions can be easily handled to construct composite filtered Lyapunov functi...

this paper is concerned with global analysis of a delay sveir epidemiological model in a population of varying size. by using lyapunov stability method and lasalle’s invariance principle for delay systems, we prove that when there is no endemic equilibrium, the disease free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally stable.

In this paper, an almost new control approach called terminal synergetic control which works based on user defined manifold is applied to a nonlinear helicopter model. Stability analysis is convestigated using Lyapunov stability theory. Synergetic controller is applied to this nonlinear fifth-order helicopter model to control height and angle. Simulation results showed that it has faster and sm...

In this paper, we discuss the synchronization and anti-synchronization of two identical chaotic T-systems. The adaptive and nonlinear control schemes are used for the synchronization and anti-synchronization. The stability of these schemes is derived by Lyapunov Stability Theorem. Firstly, the synchronization and anti-synchronization are applied to systems with known parameters, then to systems...

In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of proposed method is proved by Barbalate’s lemma. Numeri...

Abstract—This paper investigates the problem of absolute stability and robust stability of a class of Lur’e systems with neutral type and time-varying delays. By using Lyapunov direct method and linear matrix inequality technique, new delay-dependent stability criteria are obtained and formulated in terms of linear matrix inequalities (LMIs) which are easy to check the stability of the consider...

Asymptotic stability of finite-dimensional linear continuous-time periodic (FDLCP) systems is studied by the harmonic analysis. It is first shown that stability can be examined with what we call the harmonic Lyapunov equation. Another necessary and sufficient stability criterion is developed via this generalized Lyapunov equation, which reduces the stability test into that of an approximate FDL...