The concept of the exponentially stable limit cycle (ESLC) is introduced, and the ESLC phenomenon for a class of nonlinear systems is explored. Based on time-domain approach with differential inequality, the existence and uniqueness of the ESLC for such nonlinear systems can be guaranteed. Besides, the period of oscillation, the amplitude of oscillation, and guaranteed convergence rate can be a...

Problem statement: The disturbance in the complicated network of power system may cause in nonlinear response. Static Synchronous Compensator (STATCOM) is a power electronic based device that has the capability of controlling the line current. This study applies the STATCOM to decrease the over line current in power system during dynamic state. Approach: This study proposes the control strategy...

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations r t xΔ t γ Δ p t f x τ t 0 on a time scale T; here γ > 0 is a quotient of odd positive integers with r and p real-valued positive rdcontinuous functions defined on T. Our results not only extend some results established by Hassan in 2008 but also unify ...

In this paper, a novel nonlinear robust damping controller is proposed to suppress power oscillation in interconnected power systems. The proposed power oscillation damping controller exhibits good nonlinearity and robustness. It can consider the strong nonlinearity of power oscillation and uncertainty of its model. First, through differential homeomorphic mapping, a mathematical model of the s...

We prove oscillation theorems for the nonlinear delay differential equation

nowadays, atomic force microscope is considered as a useful tool in the determination of intermolecular forces and surface topography with the resolution of nanometers. in this kind of microscope, micro cantilever is considered as the heart of the microscope and is used as a measuring tool.  this paper is aimed towards investigating the behavior of a piezoelectric micro cantilever with a triang...

in this paper, newton harmonic balance method (nhbm) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. periodic solution is analytically verified and consequently the relation between the natural frequency and the amplitude is obtained in an ana...

Patients with Parkinson's disease exhibit tremor, involuntary movement of the limbs. The frequency spectrum of tremor typically has broad peaks at "harmonic" frequencies, much like that seen in other physical processes. In general, this type of harmonic structure in the frequency domain may be due to two possible mechanisms: a nonlinear oscillation or a superposition of (multiple) independent m...