On the stability of linear systems with fractional-order elements

Archives of Electrical Engineering

2016

“…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

Archives of Electrical Engineering

2016

“…The positive fractional linear systems have been investigated in [6][7][8]. The stability is a basic notion of the analysis of dynamical linear and nonlinear systems [2,[9][10][11]. Stability of fractional linear continuous-time systems has been investigated in the papers [3,12,10,[13][14].…”

Section: Introductionmentioning

confidence: 99%

“…The stability is a basic notion of the analysis of dynamical linear and nonlinear systems [2,[9][10][11]. Stability of fractional linear continuous-time systems has been investigated in the papers [3,12,10,[13][14]. The notion of practical stability of positive fractional linear systems has been introduced in [15].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Bulletin of the Polish Academy of Sciences Technical Sciences

2017

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

Minimum Energy Control of Fractional Descriptor Discrete‐Time Linear Systems with Bounded Inputs Using The DRAZIN Inverse

Asian Journal of Control

2017

The Drazin inverse of matrices is applied to solve the minimum energy control problem of fractional descriptor discrete-time linear systems with bounded inputs. Necessary and sufficient conditions for the reachability of fractional descriptor linear systems are established. The minimum energy control problem for the fractional descriptor systems with bounded inputs is formulated and solved. A procedure for the computation of the optimal inputs sequence and the minimal value of the performance index is proposed.