Sharif Digital Repository

In this paper, an oscillatory condition is obtained for fractional order relay feedback systems. This condition is derived by time domain representation of the response of the fractional order relay feedback system on the basis of the Mittag-Leffler functions. Also, using an inequality, which has been recently proved for fractional derivative of convex Lyapunov functions, an invariant set is found for the under-study fractional order relay feedback system. The obtained results are validated by numerical examples  

Oscillatory condition in LTI dynamic systems is generally expressed as possessing purely imaginary solutions by their characteristic equations. Dealing with the class of fractional order systems, such a condition is equivalently restated as owing complex roots with specific arguments by a polynomial defined based on the system characteristic equation. The degree of this polynomial can be unboundedly high. Consequently, such statement for the oscillatory condition in fractional order systems, which is based on arguments of the roots of a polynomial with an unbounded degree, cannot be viewed as a closed-form expression. To tackle this challenge, this brief introduces an approach to obtain a... 

The present study examines Alternating Current (AC) electroosmotic flows in a parallel plate microchannel subject to constant wall temperature. Numerical method consists of a central finite difference scheme for spatial terms and a forward difference scheme for the temporal term. Asymmetric boundary conditions are assumed for Poison-Boltzmann equation for determining the electric double layer (EDL) potential distribution. The potential distribution is then used to evaluate the velocity distribution. The velocity distribution is obtained by applying slip boundary conditions on the walls which accounts for probable hydrophobicity of surfaces. After determining the velocity distribution...