Reachability of Cone Fractional Continuous-Time Linear Systems

Kaczorek, Tadeusz

doi:10.2478/v10006-009-0008-4

Cited by 22 publications

(19 citation statements)

References 14 publications

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“…The fractional continuous-time linear system that is used to model the supercapacitor has been simulated also in MATLAB environment. In the simulation experiment, the system solution expressed by the Mittag-Leffler matrix function has been utilized (see e.g., [31]). The number of samples in sum operation in the calculation of the Mittag-Leffler matrix function has been limited to 150.…”

Section: Identification Methodsmentioning

confidence: 99%

Fractional-order models of the supercapacitors in the form of RC ladder networks

Mitkowski¹,

Skruch²

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. In the paper, mathematical models of the supercapacitors are investigated. The models are based on electrical circuits in the form of RC ladder networks. The elementary cell of the network may consist of resistances and capacitances that are connected in series or parallel. The dynamic behavior of the circuit is described using fractional-order differential equations and its properties are analyzed. The identification procedure with quadratic performance index is performed in time domain to identify the parameters of the supercapacitor models. The results of numerical simulations are compared with the results measured experimentally in the physical system. In addition, an example from the automotive industry is used for an experimental evaluation of the theoretical analysis and to present a perspective on the applicability of the approach for other industrial projects.

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Section: Identification Methodsmentioning

confidence: 99%

Fractional-order models of the supercapacitors in the form of RC ladder networks

Mitkowski¹,

Skruch²

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…We use three types of forward differences: the fractional Riemann-Liouville type difference defined in [5], fractional Caputo type difference defined in [9,10] and fractional Grünwald-Letnikov type difference presented in [2,[11][12][13]. The obtained results are based on [14,15].…”

Section: Introductionmentioning

confidence: 99%

Local controllability of nonlinear discrete-time fractional order systems

Mozyrska¹,

Pawłuszewicz²

2013

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The Riemann-Liouville, Caputo and Grünwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps.

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“…12 and 13 together with X 0 ∈ K P . If there exists a feedback law (14) such that for every x ∈ K P , it holds…”

Section: Corollary 12mentioning

confidence: 99%

“…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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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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Reachability of Cone Fractional Continuous-Time Linear Systems

Cited by 22 publications

References 14 publications

Fractional-order models of the supercapacitors in the form of RC ladder networks

Fractional-order models of the supercapacitors in the form of RC ladder networks

Local controllability of nonlinear discrete-time fractional order systems

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

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