Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

Busłowicz, M.; Ruszewski, Andrzej

doi:10.2478/v10006-012-0030-9

Cited by 12 publications

(9 citation statements)

References 16 publications

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“…The main purpose of this paper is to present new computational methods for checking the condition (6) of asymptotic stability of the model (1) which do not require a priori knowledge of the characteristic bivariate polynomial (5).…”

Section: Problem Formula Onmentioning

confidence: 99%

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Computer aided methods for stability analysis of 2D linear systems described by the first Fornasini-Marchesini model

Busłowicz¹,

Ruszewski²

2014

JAMRIS

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Section: Problem Formula Onmentioning

confidence: 99%

“…It is easy to see that conditions (9) and (10) can be written in the forms (7) and (8), respectively. Lemma 1.…”

Section: Solu On Of the Problemmentioning

confidence: 99%

Computer aided methods for stability analysis of 2D linear systems described by the first Fornasini-Marchesini model

Busłowicz¹,

Ruszewski²

2014

JAMRIS

Self Cite

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“…Secondly, compared with continuous-time models, the advantage they offer is that they are generally more direct, more convenient and more accurate to formulate. Thirdly, recent works have shown that for discrete-time models the dynamics can produce a much richer set of patterns than those observed in continuous-time models (Busłowicz, 2010;Busłowicz and Ruszewski, 2012;Duda, 2012;Feedman, 1980;Holling, 1965;Huang and Xiao, 2004;Hsu, 1978;Raja et al, 2011;Xu et al, 2011;Zhang et al, 2011). At last, we can get more interesting dynamical behaviors and more accurate numerical simulations results from the discrete-time models; moreover, numerical simulations of continuous-time models are obtained by discretizing the models.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response

Chen¹,

Teng²,

Hu³

2013

International Journal of Applied Mathematics and Computer Science

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The dynamics of a discrete-time predator-prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.

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“…There are fruitful achievements on this item in the past decades. To list some of these, Buslowicz (2010aBuslowicz ( , 2010b, Kaczorek (2011aKaczorek ( , 2011b discussed the stability and robust stability of positive 2-D continuous-discrete systems in general model, and Buslowicz and Ruszewski (2012) gave the computer methods for stability analysis of the Roesser type model of 2-D continuousdiscrete linear systems. Xiao in (2001aXiao in ( , 2001bXiao in ( , 2001cXiao in ( , 2003 investigated the stability and robust stability test for 2-D continuous-discrete linear systems in Roesser model, FM model and recursion model, respectively.…”

Section: Introductionmentioning

confidence: 99%

Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma

Wang

Gao

et al. 2015

Multidim Syst Sign Process

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This paper investigates the problem of stability and robust stabilization of two-dimensional (2-D) continuous-discrete systems in Roesser model. Based on KalmanYakubovich-Popov (KYP) lemma, sufficient conditions of stability of the systems are proposed in terms of linear matrix inequalities (LMIs). Moreover, combining generalized KYP lemma with frequency-partitioning idea, the conservativeness of the stability conditions may be further reduced. Robust stabilization using state feedback is studied as well and stabilizing feedback gain matrices are constructed based on the solutions of certain LMIs. In addition, the stability analysis of a class of differential repetitive processes, a special case of 2-D continuous-discrete systems in Roesser model, can adopt the results in this manuscript. Numerical examples are presented to verify the effectiveness of the method.

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Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

Cited by 12 publications

References 16 publications

Computer aided methods for stability analysis of 2D linear systems described by the first Fornasini-Marchesini model

Computer aided methods for stability analysis of 2D linear systems described by the first Fornasini-Marchesini model

Bifurcation and control for a discrete-time prey–predator model with Holling-IV functional response

Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma

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