Some Problems about Structural Properties of Positive Descriptor Systems

Bru, Rafael; Coll, Carmen; Romero‐Vivó, Sergio; Sánchez, Elena

doi:10.1007/978-3-540-44928-7_32

Cited by 54 publications

(51 citation statements)

References 5 publications

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“…4 We can reformulate conditions (21) in the variables H and H as a unique standard LP problem by using the vec and Kronecker operations as it was done previously for the LP problem (9).…”

Section: Theorem 53 Systemmentioning

confidence: 99%

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Positivity of discrete singular systems and their stability: An LP-based approach

Rami

Napp

2014

Automatica

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In this paper we present an efficient approach to the analysis of discrete positive singular systems. One of our main objectives is to investigate the problem of characterizing positivity of such systems. Previously, this issue was not completely addressed. We provide easily checkable necessary and sufficient conditions for such problem to be solved. On the other hand, we study the stability of discrete positive singular systems. Note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone. All the conditions we provide are necessary and sufficient, and are based on a reliable computational approach via linear programming.

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“…4 We can reformulate conditions (21) in the variables H and H as a unique standard LP problem by using the vec and Kronecker operations as it was done previously for the LP problem (9).…”

Section: Theorem 53 Systemmentioning

confidence: 99%

“…To the best of our knowledge few works on such systems can be found in the literature [4,5,10,18,19,29,36]. These works are based on a common standing, but unnecessary, assumption for positivity of a singular system.…”

Section: Introductionmentioning

confidence: 99%

Positivity of discrete singular systems and their stability: An LP-based approach

Rami

Napp

2014

Automatica

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“…Descriptor (singular) linear systems have been considered in many papers and books [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The eigenvalues and invariants assignment by state and output feedbacks have been investigated in [4,15,18] and the minimum energy control of descriptor linear systems in [19,21].…”

Section: Introductionmentioning

confidence: 99%

Fractional descriptor standard and positive discrete-time nonlinear systems

Kaczorek¹

2015

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract.A method of analysis of the fractional descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and demonstrated on a numerical example.

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“…Descriptor (singular) linear systems have been considered in many papers and books (Bru et al, 2003;2002;Choundhury, 1972;Campbell et al, 1976;Dai, 1989;Guang-Ren Duan, 2010;Kaczorek, 2013;2011a;2014b;2004;1992;2014c;2011c;2011d;2011e;Virnik, 2008). The eigenvalue and invariant assignment by state and output feedbacks was investigated by Kaczorek (2004;2011d), along with minimum energy control of descriptor linear systems (Kaczorek, 2014b).…”

Section: Introductionmentioning

confidence: 99%