Fractional Positive Continuous-Time Linear Systems and Their Reachability

In the paper, fractional discrete cone control systems with n-orders are considered. Some relations between invariance and (asymptotic) stability properties of the presented systems are discussed. Operators employed to the considered systems are Caputo-, Riemman-Louville-, and Grünwald-Letnikov type ones. Cone systems with control, which are particular invariant systems with control, together with their stability and asymptotic stability properties are examined.

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“…is called a linear cone of state generated by the matrix P in R n (see [12,14]). If X n := {X : N 0 → R n }, then the set…”

Section: Cone Systemsmentioning

confidence: 99%

Remarks on Fractional Discrete Cone Control Systems with n-Orders and Their Stability

Girejko

Pawłuszewicz

2016

J Dyn Control Syst

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“…Observers for fractional linear systems were addressed by Kaczorek (2008), Kociszewski (2013) and Vinagre et al (2002), and for descriptor linear systems by Kaczorek (2014a). Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems were proposed by Kaczorek (2001), along with reduced-order observers (Kaczorek, 2014b).…”

Section: Introductionmentioning

confidence: 99%

Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

Kaczorek

2016

International Journal of Applied Mathematics and Computer Science

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“…The positive linear systems consisting of n subsystems with different fractional orders have been addressed in [17]. The controllability and minimum energy control of fractional systems have been analyzed in [18][19][20] and the reachability of fractional positive linear systems in [18].…”

Section: Introductionmentioning

confidence: 99%

Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers

Kaczorek

2017

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The stability of fractional standard and positive continuous-time linear systems with state matrices in integer and rational powers is addressed. It is shown that the fractional systems are asymptotically stable if and only if the eigenvalues of the state matrices satisfy some conditions imposed on the phases of the eigenvalues. The fractional standard systems are unstable if the state matrices have at least one positive eigenvalue.Key words: stability, fractional, positive, linear, continuous-time, system, integer, rational, order. Stability of fractional positive continuous-time linear systemswith state matrices in integer and rational powers The following notation will be used: ℜ -the set of real numbers, ℜ n×m -the set of n×m real matrices, ℜ + n×m -the set of n×m real matrices with nonnegative entries and ℜ + n = ℜ + n×1 , M n -the set of n×n Metzler matrices (real matrices with nonnegative off-diagonal entries), I n -the n×n identity matrix. PreliminariesConsider the fractional autonomous continuous-time linear system BULLETIN OF THE POLISH ACADEMY OF SCIENCES TECHNICAL SCIENCES, Vol. XX, No. Y, 2016 DOI: 10.1515/bpasts-2016 Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers

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Fractional Positive Continuous-Time Linear Systems and Their Reachability

Cited by 173 publications

References 17 publications

Remarks on Fractional Discrete Cone Control Systems with n-Orders and Their Stability

Remarks on Fractional Discrete Cone Control Systems with n-Orders and Their Stability

Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems

Stability of fractional positive continuous-time linear systems with state matrices in integer and rational powers

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