Input–output finite-region stability and stabilization for discrete 2-D Fornasini–Marchesini models

Zhang, Guangchen; Trentelman, Harry L.; Wang, Weiqun; Gao, Jingbo

doi:10.1016/j.sysconle.2016.10.011

Cited by 27 publications

(7 citation statements)

References 32 publications

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“…All computations were performed with Maple. Example 1: Let us consider the 2D system described by (1) where…”

Section: Numerical Examples and Applicationmentioning

confidence: 99%

“…Two dimensional systems are a class of dynamic systems which propagate information in two independent directions. This propagation feature makes 2D system's dynamics depend upon two independent variables [1]. That make the analysis of 2D systems much more complicated and difficult than common one-dimensional (1D) systems, especially for uncertain 2D system [1], [2].…”

Section: Introductionmentioning

confidence: 99%

“…This propagation feature makes 2D system's dynamics depend upon two independent variables [1]. That make the analysis of 2D systems much more complicated and difficult than common one-dimensional (1D) systems, especially for uncertain 2D system [1], [2]. Recently, the heightened research interest in the study of 2D systems can be attributed to its widespread applications in processing 2D sampled data, such as seismic data, photogrammetric data [1], [3]- [6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Design of Parametric Controller for Two-Dimensional Polynomial Systems Described by the Fornasini-Marchesini Second Model

Hou

2019

IEEE Access

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In this paper, a general parametric controller design method is presented for twodimensional (2D) linear discrete systems described by the Fornasini-Marchesini second model. This method is based on the discriminant systems of polynomial and Hurwitz theorem. By the fractional linear transformation, the problem of stability analysis for 2D systems can be turned to a new problem whether the polynomials are Hurwitz stable. Thus, the process of stability analysis is changed into a problem whether some polynomials are positive definite, which can be easily checked by the discriminant system of the polynomial. It simplifies some existing methods of analyzing stability for 2D systems. Then, we apply the process proposed stability analysis method to consider the stabilization problem. A parametric controller is derived. The form of the parametric controller designed by the proposed method is simple, the parameters of the controller law can be fully solved. Finally, we give two numerical examples and a practical example of a chemical reactor thermal process to show the validity of the proposed methods.INDEX TERMS Parametric controller, 2D system, the Fornasini-Marchesini second model, the discriminant system of polynomial.

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“…All computations were performed with Maple. Example 1: Let us consider the 2D system described by (1) where…”

Section: Numerical Examples and Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Design of Parametric Controller for Two-Dimensional Polynomial Systems Described by the Fornasini-Marchesini Second Model

Hou

2019

IEEE Access

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“…Research has also been reported on finite region stability and stabilization of 2D linear systems, where for systems described by (2), a finite region is defined, for a finite positive integer N, as {(i, j) : i + j ≤ N, and N . Recent results include Zhang, Trentelman, Wamg, and Gao (2017). This formulation includes iterative learning control where the trial length is finite and in applications only a finite number of trials will ever be completed.…”

Section: Other Systems Theoretic Analysismentioning

confidence: 99%

Control systems analysis for the Fornasini-Marchesini 2D systems model – progress after four decades

Gałkowski

Rogers

2018

International Journal of Control

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The development of a control systems theory for multidimensional linear systems, i.e., systems with more than one independent variable is an area where a very significant volume of research is based on representations for the underlying dynamics introduced in the 1970s. One of these is the Fornasini-Marchesini state-space model published in 1978. This paper reviews the significant developments in the succeeding four decades in both theory and application, where the second area includes examples where this model description is an enabler the analysis of other classes of systems.

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“…On the other hand, significant progress has been made in the theory of regional stability [22‐27]. The problem of regional stability analysis of two‐dimensional nonlinear polynomial systems represented by the Fornasini–Marchesini second state‐space model was addressed in Osowsky et al [22].…”

Section: Introductionmentioning

confidence: 99%

Regional stability analysis of impulsive switched nonlinear systems with multiple equilibrium points

Wang

Feng

2020

Asian Journal of Control

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This paper addresses the regional stability problem for impulsive switched nonlinear systems (ISNSs) whose subsystems have more than one equilibrium point, that is, multiple equilibrium points (MEPs) coexist. Meanwhile, we derive analytical results and sufficient conditions about the regional stability. Through investigating the dynamical behavior of ISNSs with MEPs, the multiple Lyapunov functions (MLFs) method is established for the regional stability. It is shown that main results obtained in this paper not only guarantee the regional stability of ISNSs with MEPs under arbitrary switching signals but also provide a new method to determine the corresponding stable regions for the regional stability. Numerical simulations are given to illustrate and verify advantages of our proposed results.

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Input–output finite-region stability and stabilization for discrete 2-D Fornasini–Marchesini models

Cited by 27 publications

References 32 publications

Design of Parametric Controller for Two-Dimensional Polynomial Systems Described by the Fornasini-Marchesini Second Model

Design of Parametric Controller for Two-Dimensional Polynomial Systems Described by the Fornasini-Marchesini Second Model

Control systems analysis for the Fornasini-Marchesini 2D systems model – progress after four decades

Regional stability analysis of impulsive switched nonlinear systems with multiple equilibrium points

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