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
On the other hand, our formalism includes the description of a discrete-time system
based on the difference operator description (delta-domain approach), for which the results shown in the paper are new, since previous results have been obtained for discrete-time systems
considered on the basis of the shift-operator formalism.
If T = N, then x is a discrete-time system
and, as we notice in the above discussion, there exists a unique (forward) solution of (5.
Klee (University of Central Florida) derives mathematical models of continuous-time systems and the discrete-time system
models created to simulate them.
In doing so one has to assume that the state transition map of the discrete-time system
is reversible, the property not necessarily satisfied automatically in the discrete-time case, except for models obtained by sampling the continuous-time systems .
Therefore, note that since the shift operator is not a delta-derivative, the time scale formalism accommodates the discrete-time system
description in terms of the difference operator, in opposition to more conventional models based on the shift operator [1,6].
k] for a discrete-time system
, only the files Core, Ore polynomials, and Sequences are loaded.
From a modelling point of view, dynamical systems on time scales incorporate both continuous- and discrete-time systems
as special cases, allowing us to unify the study and consider the classical results as special cases from the new theory.
They cover transfer functions and frequency responses, controlability and observability, the stationary stabilization of linear systems, the non-stationary low-frequency and high-frequency stabilization of linear systems, and stabilizing discrete-time systems
Monotonically convergent iterative learning control for linear discrete-time systems