A discrete ordered set of observed data that changes over time is called a time series and denoted as (y(t) = { y(t_{1}), y(t_{2}), ldots,y(t_{i}), ldots }), where (y(t_{i})) is the observed data at the moment (t _{i}).
Many heritable traits, from pathogen resistance in plants [1] to panic disorder in humans [2], are described using discrete categories such as color or are quantified using discrete, ordered scales such as "mildly," "moderately," or "severely" affected.
OGTT values are discrete, ordered measurements from an underlying, continuous process; i.e. an individual's glucose regulation.
The second dependent variable is instead modelled as a discrete ordered variable (IntentionToUse) taking values 1, 2 and 3 for subjects reporting to be 'not likely'quiteite likely' and 'likely' to use the websites in the future, respectively.
Figure 1 shows a schematic: translation determines a series of amino acid sequences {.., Seqt−1, Seqt, Seqt+1,.} = {Seqt}t∈Z, each Seqt for one protein chain, ordered by a discrete temporal order t∈Z of corresponding tertiary structures {.., Strt−1, Strt, Strt+1,.} = {Strt}t∈Z, where Z = {..,−1, 0, 1,.} is the set of integers.
The mathematical methods needed for computations in engineering and the sciences must be transformed from the continuous to the discrete in order to be carried out on a computer.
The discrete fractional order state space system is first recalled.
Clearly, system (5) is also a discrete second order Hamiltonian system.
The paper is devoted to the design of an Luenberger-type observer for discrete fractional order systems.
