In this paper, we have exploited the first-order sliding mode control method to track the ECG data of the human heart by three different nonlinear control laws. In order to lessen the intrinsic chattering of the classic sliding mode control system, smooth function approximations of the control input, by means of the hyperbolic tangent and the saturation function, were used. The fast Fourier tra...

In this paper, we propose an optimized method for nonlinear function approximation based on multiplierless piecewise linear computation (ML-PLAC), which call OML-PLAC. OML-PLAC finds the minimum number of segments with predefined fractional bit width input/output, maximum shift-and-add operations, user-defined widths intermediate data, and absolute error (MAE). addition, minimizes actual MAE as...

The main objective of this paper is to establish several new lower and upper bounds for the functions $\sinh x/x$ $\cosh x$. Following simple approach, our results give refinements generalizations some known inequalities involving these functions.

We consider an autonomous system admitting invariant manifold M. The following questions are discussed: (i) what the conditions ensuring exponential stability of manifold? (ii) does every motion attracting by M tend to some on (i.e. have asymptotic phase)? (iii) is geometrical structure set formed orbits approaching a given orbit? get answer in terms Lyapunov functions omitting assumption that ...

Evolution of the main signal in a Lorentz dispersive medium is considered. The signal propagating in the medium is excited by a sine-modulated pulse signal, with its envelope described by a hyperbolic tangent function. Both uniform and non-uniform asymptotic representations for the signal are found. It is shown when the uniform representation can be reduced to the non-uniform one. The results o...