Ultracapacitor parameters identification based on fractional order model

Dzieliński, Andrzej; Sierociuk, Dominik; Sarwas, Grzegorz

doi:10.23919/ecc.2009.7074403

Cited by 47 publications

(28 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using the Kirchhoff's laws we may describe the transient states in the electrical circuits by state equations [2,4,13,20,28,29] Proof. Sufficiency.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Minimum energy control of fractional positive electrical circuits

Kaczorek

2016

Archives of Electrical Engineering

View full text Add to dashboard Cite

show abstract

“…Using the Kirchhoff's laws we may describe the transient states in the electrical circuits by state equations [2,4,13,20,28,29] Proof. Sufficiency.…”

Section: Preliminariesmentioning

confidence: 99%

“…The notion of practical stability of positive fractional linear systems has been introduced in [11]. Some recent interesting results in fractional systems theory and its applications can be found in [2,12,[29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Minimum energy control of fractional positive electrical circuits

Kaczorek

2016

Archives of Electrical Engineering

View full text Add to dashboard Cite

show abstract

“…The notion of practical stability of positive fractional linear systems has been introduced in [15]. Some recent interesting results in fractional systems theory and its applications can be found in [4,10,13,16]. The positive linear systems consisting of n subsystems with different fractional orders have been addressed in [17].…”

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

View full text Add to dashboard Cite

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

show abstract

“…The first definition of the fractional derivative was introduced by Liouville and Riemann at the end of the 19 th century [10,11] and another one was proposed in 20 th century by Caputo [12]. This idea has been used by engineers for modeling different processes [13][14][15]. Mathematical fundamentals of fractional calculus are given in the monographs [10][11][12]16].…”

Section: Introductionmentioning

confidence: 99%

Descriptor fractional discrete-time linear system with two different fractional orders and its solution

Sajewski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. Factional Discrete-time linear systems with fractional different orders are addressed. The Weierstrass-Kronecker decomposition theorem of the regular pencil is extended to the descriptor fractional discrete-time linear system with different fractional orders. Using the extension, method for finding the solution of the state equation is derived. Effectiveness of the method is demonstrated on a numerical example.

show abstract

Ultracapacitor parameters identification based on fractional order model

Cited by 47 publications

References 0 publications

Minimum energy control of fractional positive electrical circuits

Minimum energy control of fractional positive electrical circuits

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

Descriptor fractional discrete-time linear system with two different fractional orders and its solution

Contact Info

Product

Resources

About