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....

The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

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....

The neutron density is one of the most important dynamical parameters in a reactor. It is directly related to the control and stability of the reactor power. Any change in applied reactivity and some of dynamical parameters in the reactor causes a change in the neutron density. Lyapunov exponent method is a powerful tool for investigating the range of stability and the transient behavior of the...

this paper considers the problem of stable limit cycles generating in a class of uncertain nonlinear systems which leads to stable oscillations in the system’s output.this is a wanted behavior in many practical engineering problems. for this purpose, first the equation of the desirable limit cycle is achieved according to shape, amplitude and frequency of the required output oscillations. then,...

‎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.

4 Lyapunov Exponents 5 4.1 Definition and basic properties . . . . 6 4.2 Constraints on the Lyapunov exponents 7 4.3 Calculating the largest Lyapunov exponent method 1 . . . . . . . . . . . 7 4.4 Calculating the largest Lyapunov exponent method 2 . . . . . . . . . . . 8 4.4.1 Maps . . . . . . . . . . . . . . 8 4.4.2 Continuous systems . . . . . . 8 4.5 Calculating the other Lyapunov exponents ....