Practical Stability and Asymptotic Stability of Interval Fractional Discrete-Time Linear State-Space System

Ruszewski, Andrzej

doi:10.1007/978-3-319-05353-0_22

Cited by 11 publications

(5 citation statements)

References 15 publications

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“…The conditions for robust stability checking of interval systems with pure delay of natural order have been proposed in [1] for continuous-time systems and in [4], [16] for fractional interval discrete-time linear systems.…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Robust stability of a class of uncertain fractional order linear systems with pure delay

Busłowicz

Ruszewski²

2015

Archives of Control Sciences

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The paper considers the robust stability problem of uncertain continuous-time fractional order linear systems with pure delay in the following two cases: a) the state matrix is a linear convex combination of two known constant matrices, b) the state matrix is an interval matrix. It is shown that the system is robustly stable if and only if all the eigenvalues of the state matrix multiplied by delay in power equal to fractional order are located in the open stability region in the complex plane. Parametric description of boundary of this region is derived. In the case a) the necessary and sufficient computational condition for robust stability is established. This condition is given in terms of eigenvalue-loci of the state matrix, fractional order and time delay. In the case b) the method for determining the rectangle with sides parallel to the axes of the complex plane in which all the eigenvalues of interval matrix are located is given and the sufficient condition for robust stability is proposed. This condition is satisfied if the rectangle multiplied by delay in power equal to fractional order lie in the stability region. The considerations are illustrated by numerical examples.

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Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Robust stability of a class of uncertain fractional order linear systems with pure delay

Busłowicz

Ruszewski²

2015

Archives of Control Sciences

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“…In multi-inputs multi-outputs linear systems by the use of the state feedbacks we may also modify the positions of the zeros of their transfer matrices. Practical stability, asymptotical stability and robust stability have been investigated in [15,16]. Stabilization of descriptor fractional continuous-time and discrete-time systems have been analyzed in [17,18] and global stability of nonlinear feedback systems with fractional positive linear parts in [4].…”

Section: Introductionmentioning

confidence: 99%

Stability of convex linear combinations of continuous-time and discrete-time linear systems

2024

Archives of Control Sciences

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The asymptotic stability of the convex linear combination of continuous-time and discretetime linear systems is considered. Using the Gershgorin theorem it is shown that the convex linear combination of the linear asymptotically stable continuous-time and discretetime linear systems is also asymptotically stable. It is shown that the above thesis is also valid (even simpler) for positive linear systems.

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“…The stability of nonlinear continuous-time standard and fractional positive systems have been analyzed in [2,3,5,6,9,11,12,14,16,18]. The positive different orders fractional linear systems has been introduced in [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…The dynamical properties of linear systems with state Metzler matrices have been analyzed in [17]. The decentralized stabilization of descriptor fractional positive systems with delays have been investigated in [21,22] and the practical stability and robust stability of discrete-time fractional linear systems in [18,20]. The global stability of positive time-varying nonlinear feedback timevarying systems has been considered in [13].…”

Section: Introductionmentioning

confidence: 99%

Global Stability of Positive Discrete-time Time-varying Nonlinear Feedback Systems

Kaczorek

Sajewski

2021

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The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.

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Practical Stability and Asymptotic Stability of Interval Fractional Discrete-Time Linear State-Space System

Cited by 11 publications

References 15 publications

Robust stability of a class of uncertain fractional order linear systems with pure delay

Robust stability of a class of uncertain fractional order linear systems with pure delay

Stability of convex linear combinations of continuous-time and discrete-time linear systems

Global Stability of Positive Discrete-time Time-varying Nonlinear Feedback Systems

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