Robust stability of positive discrete-time linear systems of fractional order
By Mikolaj Buslowicz. 2010
47 citations recorded by the source corpus.
The paper is devoted to the problem of robust stability of linear positive discrete-time systems of fractional order with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of linear uncertainty structure with unity rank uncertainty structure and with non-negative perturbation matrices, are established. It is shown that robust stability of the positive discrete-time fractional system is equivalent to: 1) robust stability of the corresponding positive discrete-time system of natural order in the general case, 2) robust stability of the corresponding finite family of positive discrete-time systems of natural order in the case of linear unity rank uncertainty structure, 3) asymptotic stability of only one corresponding positive discrete-time system of natural order – in the case of linear uncertainty structure with non-negative perturbation matrices. Moreover, simple necessary and sufficient condition for robust stability of the positive interval discrete-time linear systems of fractional order is given. The considerations are illustrated by numerical examples.
Subfields: Computer Networks and Communications, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/ee2188c0bf67937b84a1939ff61f6ac98fdd7f6f
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In Computer Networks and Communications
In Control and Systems Engineering
Citations in the corpus
- The -Transform Method and Delta Type Fractional Difference Operators (2015, background): “One of the attempts to the stability of fractional difference systems is the notion of practical stability, see [6, 7].”
- Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders (2012, unknown): “Key words: linear system, continuous-time, fractional, stability, Mikhailov criterion.”