New stability results for 2-D discrete systems based on the Fornasini-Marchesini state space model

Kanellakis, A.

doi:10.1049/ip-cds:19941368

Cited by 8 publications

(4 citation statements)

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“…The problem of asymptotic stability of system (1) has been studied by many researchers [51][52][53][54][55][56][57][58][59]. Lyapunov based sufficient condition for the stability of system (1) has been investigated in [51] and it is proposed that the system (1) is asymptotically stable if there exist an  symmetric matrix such…”

Section: A Brief Surveymentioning

confidence: 99%

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A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

Tiwari¹,

Dhawan²

2012

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A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular model, called Forna- sini-Marchesini (FM) second model was proposed by Fornasini and Marchesini in 1978. The aim of this paper is to present a survey of the existing literature on the stability of FM second model

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Section: A Brief Surveymentioning

confidence: 99%

“…is defined in (4a). Further, based on the 2-D Lyapunov equation approach, the problem of stability margin has also been studied in [52].…”

Section: A Brief Surveymentioning

confidence: 99%

A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

Tiwari¹,

Dhawan²

2012

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“…Over the past decades, 2D systems have received considerable attention in both theoretical and practical research. On the theoretical front, the early works − focused mainly on the stability issues of linear 2D systems which are more complicated than those of the 1D case. Recently, a number of results on the robust control of 2D systems has been reported.…”

Section: Introductionmentioning

confidence: 99%

From Two-Dimensional Linear Quadratic Optimal Control to Iterative Learning Control. Paper 1. Two-Dimensional Linear Quadratic Optimal Controls and System Analysis

Shi

Gao

Tie-jun

2006

Ind. Eng. Chem. Res.

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This paper develops two-dimensional linear quadratic (2DLQ) optimal control schemes that can be applied for iterative learning control (ILC) design. For a class of repetitive 2D processes, based on control objectives defined over a single cycle or multiple cycles, two different 2DLQ optimal control schemes, single-cycle 2DLQ (SC-2DLQ) and multicycle 2DLQ (MC-2DLQ), are derived. Furthermore, to balance control performance and computational load of MC-2DLQ optimal control, a cyclewise receding horizon 2DLQ (CWRH-2DLQ) optimal control strategy is introduced based on a quadratic performance index with a cyclewise receding horizon. The cyclewise stability and robustness analysis are conducted based on the cyclewise dynamics of the closed-loop system. The simulation shows that the proposed algorithms are effective. On the basis of the results of this paper, new ILC schemes for batch processes will be presented as a sequel to this paper.

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“…It is shown there that the matrix P ( j 𝛽) can be transformed in the Schwarz form with complex elements, see (37). The sufficient and necessary conditions for stability are given by 𝛿 𝜆 (𝛽) > 0, 𝛽 ∈ R ∪ {∞}, 𝜆 = 1, 2, … , (n + m) (38) Consider the matrix Lyapunov equation with complex elements given in (35). We choose…”

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confidence: 99%

Stability analysis of 2‐D discrete and continuous state‐space systems

Kanellakis

Tawfik

Agathoklis

2021

IET Control Theory & Appl

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This paper presents new stability conditions for two-dimensional (2-D) systems in statespace description. Both discrete and continuous systems are studied. These results are based on the criteria first presented by Huang, De Carlo, Strintzis, Murray, Delsarte, et al. and on the discrete Lyapunov equation with complex elements for 2-D systems. The stability properties of the Mansour matrix are also used for stability testing in state-space. Criteria for the VSHP property of 2-D polynomials are further presented using the continuous Lyapunov equation with complex elements and the stability properties of the Schwarz matrix form. The stability properties of the Schwarz matrix are also used for testing the VSHP property of 2-D polynomials in state-space. The proposed new criteria are nonconservative for the stability analysis of 2-D discrete and continuous systems and achieve the aim of reducing the original 2-D problem as much as possible to a set of 1-D stability tests. Numerical examples are given to illustrate the utility of the proposed conditions.

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New stability results for 2-D discrete systems based on the Fornasini-Marchesini state space model

Cited by 8 publications

References 0 publications

A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

From Two-Dimensional Linear Quadratic Optimal Control to Iterative Learning Control. Paper 1. Two-Dimensional Linear Quadratic Optimal Controls and System Analysis

Stability analysis of 2‐D discrete and continuous state‐space systems

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