The reason is that under a simple additional assumption (besides commensurable delays), a discrete-time system
with delays can be transformed into a higher dimensional discrete-time system
without delays and thus, one can apply the standard theory to such systems.
Bartoszewicz designed a quasi-sliding-mode controller for a discrete-time system
in  that can reduce chattering caused by high frequency.
Readers should be well acquainted with foundations of the power electronics discipline, along with associated continuous-time modeling and control techniques; familiarity with sampled-data and discrete-time system
analysis would be helpful but is not absolutely necessary.
Such assumption does not pose any real difficulty due to the fact that, by relabeling the states, any discrete-time system
can easily be transformed into an equivalent system such that (5a) and 5b) hold.
Dynamical, linear discrete-time system
can be described by finite set of coefficients of difference equations or state space model.
Remark 1: The special class of discrete-time bilinear systems to be considered in this paper is the class where the discrete-time system
can be described as in (1).
1 gives a sufficient condition for stability criterion for discrete-time system
Consider the nonlinear discrete-time system
described by a set of first-order difference equations of the form
When d = 1, [tau] = [tau] = [gamma]T, the augmented discrete-time system
of Equation (1) which accommodates the input delay can be represented as
Consider the discrete-time system
of the following form
Kato, "Design of an optimal controller for a discrete-time system
subject to previewable demand," International Journal of Control, vol.
The convergence of the algorithm is considered for the following dynamical nonlinear discrete-time system