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

Tiwari, Manish; Dhawan, Amit

doi:10.4236/cs.2012.31003

Cited by 11 publications

(4 citation statements)

References 56 publications

(75 reference statements)

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“…Transfer function for the General model is given as: , then equation (1.1) become the FM second state-space model [8].…”

Section: Preliminariesmentioning

confidence: 99%

“…The state-space methods have long outlived the other conventional methods to represent and analyze the practical systems. Motivated by this, many authors have attempted to describe the 2-D filter behavior in terms of linear state-space models [4][5][6][7][8]. In this paper, we consider the 2-D General state-space model [9] because many other popular state-space models can be represented as a special case of the General model.Rapid developments in VLSI design and computing technology have attracted many researchers [10-13] to study and analyze the hardware architectures for 2-D state-space filtering.…”

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confidence: 99%

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Hardware Realization of 2-D General Model State Space Systems

Shrivastava¹,

Kumar²,

Tiwari³

2017

IJET

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In this paper, a hardware oriented realization, for the real time two dimensional (2-D) state space general model systems, is proposed. The proposed design of 2-D systolic array utilizes processing elements (PEs) which is simpler in use. The number of PEs is made equal to the multiplication of both the number of rows and column of the considered architecture. The proposed architecture provides excellent performance in terms of speed, efficiency and accuracy. Further, different designs of PEs are also proposed for state space feedback controller and unified structure. The unified structure can be work as state space systems as well as feedback controller after applying some control signals. It is shown that the area of unified structure is slightly more than that of structure-I and II taken separately. The ASIC synthesis results shows the proposed unified structure for system/controller of order 7 has taken approx 22% more area and 50% less area than state space system and controller with feedback respectively. Finally, the proposed architecture is implemented and analyzed using Verilog-HDL and Synopsis Design Compiler with 90nm TSMC target libraries.Keyword -2-D system, FM model, General model, state space filter realization, Synopsis Design Compiler, Verilog.I. INTRODUCTION The recent past have seen a continuously going research interests in the area of two-dimensional (2-D) discrete systems, due to their theoretical and practical viability in many application areas such as weather signal, seismographic data processing signal, mechanical vibration signal, remote sensing and telemetry signals, radio astronomy signal, biomedical system, navigation signals, gas absorption, water stream heating, radar and mobile signals etc. [1][2][3]. In a 2-D discrete system, information propagates in two independent directions, thereby making the system dynamics a function of two independent integer variables. The state-space methods have long outlived the other conventional methods to represent and analyze the practical systems. Motivated by this, many authors have attempted to describe the 2-D filter behavior in terms of linear state-space models [4][5][6][7][8]. In this paper, we consider the 2-D General state-space model [9] because many other popular state-space models can be represented as a special case of the General model.Rapid developments in VLSI design and computing technology have attracted many researchers [10-13] to study and analyze the hardware architectures for 2-D state-space filtering. In [10], high speed VLSI architecture is proposed for the realization of 2-D recursive filters. The Local state-space realization of the generalized 2-D filter transfer function is obtained by mapping its signal flow graph to the 2-D state-space model. The 2-D recursive digital filter represented by a 2-D block state-space model is considered in [11] and a pipelined SIMD architecture is developed for the purpose of 2-D block processing. This type of architecture is particularly useful when similar operations on a large set of da...

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“…Transfer function for the General model is given as: , then equation (1.1) become the FM second state-space model [8].…”

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

Hardware Realization of 2-D General Model State Space Systems

Shrivastava¹,

Kumar²,

Tiwari³

2017

IJET

Self Cite

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“…The two‐dimensional (2D) system was first introduced in 1970s, whose information is propagated along two independent directions 1,2 . From then on, there is increasing interest in researching of 2D systems due to its wide applications in practical systems 1,3 .…”

Section: Introductionmentioning

confidence: 99%

H_∞ tracking control of two‐dimensional fuzzy networked systems

Tanaka

Chai

et al. 2020

Optim Control Appl Methods

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Summary In this article, the H∞ tracking control problem is first considered for two‐dimensional fuzzy networked control systems. The system is described by fuzzy blending of the so‐called second Fornasini‐Marchesini local linear state‐space model. Based on the fuzzy model, an observer‐based state feedback controller is employed to guarantee the H∞ tracking performance. The separation property is established in the case of observer‐based H∞ tracking control framework, that is, the controller gains and observer gains can be simultaneously obtained by solving two sets of linear matrix inequalities. A simulation example is given to illustrate the effectiveness of the proposed method.

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“…Two-dimensional (2D) systems are attracting significant attention from the research community, due to the presence of this class of systems in water stream heating, seismographic data processing, thermal processes, multidimensional digital filtering, process control, image and signal processing, etc [13,16,15,17]. Among the relevant results already published, the stability of 2D systems has been studied in, for example, [10,12,21,23]; the stabilization of 2D systems has been explored in [25,9,18,11]. This paper concentrates on 2D singular systems which have been studied in the few past decades and which could have various practical applications in many areas such as: digital filtering, modeling and control of electrical circuits, power systems, economics etc.…”

Section: Introductionmentioning

confidence: 99%

Stability and Stabilization of 2D Singular Systems: A Strict LMI Approach

Elloumi

Ghamgui

Mehdi

et al. 2019

Circuits Syst Signal Process

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This paper deals with the stability and stabilization of 2D singular systems described by a Roesser model. The proposed results are presented in terms of a strict Linear Matrix Inequality (LMI), which makes possible to elaborate a new sufficient admissibility condition. Based on this condition the design of a state feedback controller is also treated, deriving a sufficient condition for the admissibility of the closed loop system. A numerical example is given at the end of the paper to illustrate the effectiveness of the proposed methodology.

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

Cited by 11 publications

References 56 publications

Hardware Realization of 2-D General Model State Space Systems

Hardware Realization of 2-D General Model State Space Systems

H_∞ tracking control of two‐dimensional fuzzy networked systems

Stability and Stabilization of 2D Singular Systems: A Strict LMI Approach

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

Cited by 11 publications

References 56 publications

Hardware Realization of 2-D General Model State Space Systems

Hardware Realization of 2-D General Model State Space Systems

H∞ tracking control of two‐dimensional fuzzy networked systems

Stability and Stabilization of 2D Singular Systems: A Strict LMI Approach

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H_∞ tracking control of two‐dimensional fuzzy networked systems