‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

We show the existence of a local stable manifold for a bidirectional discrete-time nondiffeomorphic nonlinear Hamiltonian dynamics. This is the case where zero is a closed loop eigenvalue and therefore the Hamiltonian matrix is not invertible. In addition, we show the eigenstructure and the symplectic properties of the mixed direction nonlinear Hamiltonian dynamics. We extend the Local Stable M...

In this paper, the fault detection problem for nonlinear dynamic power systems based an observer is treated. The nonlinear dynamic model based on differential algebraic equations (DAE) is transformed in to ordinary differential equations (ODE). Three nonlinear observers are used and compared for generating the residual signals. Which are: the extended Kalman filter, the extended Kalman estimato...