Fractional Discrete-time Research Articles

Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems

Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear SystemsIn the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical examples.

Reachability and controllability to zero tests for standard and positive fractional discrete-time systems

The reachability and controllability to zero of standard and positive fractional linear discrete-time systems are addressed. Necessary and sufficient conditions for the controllability of standard fractional discrete-time systems are established. New tests for checking the reachability and controllability to zero of the standard fractional systems are presented. A notion of positive fractional linear discrete-time systems is introduced. Necessary and sufficient conditions for the positivity, reachability and controllability to zero of fractional discrete-time systems are given.

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Fractional Discrete-Time Signal Processing: Scale Conversion and Linear Prediction

A generalization of the linear prediction for fractional steps isreviewed, widening well-known concepts and results. This prediction isused to derive a causal interpolation algorithm. A reconstructionalgorithm for the situation where averages are observed is alsopresented. Scale conversion of discrete-time signals is studied takingas base the fractional discrete-time system theory. Some simulationresults to illustrate the behaviour of the algorithms will be presented.A new algorithm for performing the zoom transform is also described.