The KF is an optimal state estimation method for a stochastic signal [29] that estimates the state of a discrete-time controlled process,, with measurement data, where and are governed by the linear stochastic difference equations: (3).
Next, the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion (LDI).
The system controlled by the saturating control law is modelled by a linear difference inclusion.
In the third section we will present another way for dealing with the unique existence problem by using only the theory of linear difference equations.
In [4, 5] the authors study linear difference equations perturbed by Volterra terms.
Trench [39] introduced summable similarity as a discrete analog of Conti's definition of t ∞ -similarity and investigated the various stabilities of linear difference systems by using summable similarity.
On the other hand, we know that the polynomial equations of order greater than or equal to five need not be solved by radicals, which implies that there are linear difference equations with constant coefficients for which we cannot find a closed-form formula for their general solutions.
With Euler's method, a non-autonomous system is approximated by a non-linear difference system and then an approximate global Poincaré map function is derived from the difference system by iterating one or more periods of a periodic excitation.
The analytical vibration solutions for lattice model or FDM can be obtained by solving the linear second-order finite difference equation derived herein.
The linear system of difference equations have been solved by the block Gauss elimination method and the non-linear system of difference equations by the block Newton's method in which we have considered (y_{0}=0) as the initial approximation.
