A survey on stability of 2-D discrete systems described by Fornasini-Marchesini first model

Tiwari, Manish; Dhawan, Amit

doi:10.1109/icpces.2010.5698674

Cited by 4 publications

(7 citation statements)

References 42 publications

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“…which, in turn, implies the constraint (ii) in (26). Thus, the minimization of    implies the minimization of the guaranteed cost in (21). This completes the proof of Theorem 3.2.…”

supporting

confidence: 60%

“…In [20], necessary and sufficient conditions for the asymptotic stability of the FM first model using non-negative matrix theory have been proposed, and it has been shown that the conditions are sharper than those reported in [10,11,17]. Further, a survey of the existing literature on the stability of the 2-D discrete systems described by FM first model has been presented in [21].…”

Section: Introductionmentioning

confidence: 99%

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Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

Tiwari¹,

Dhawan²

2012

JSIP

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This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function

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supporting

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

Tiwari¹,

Dhawan²

2012

JSIP

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“…Thus, in this section we consider a unified structure which is suitable for a variety of data processing and control applications. A comparison between the architecture of PEs of Figure (3b) and Figure (6) shows that difference lies in the inputs given to various MMTUs. In order to solve the issue in a simplified manner we introduce a multiplexer which selects input that is feeded to MAT MUL-4, MAT MUL-5 and MAT MUL-6 blocks of Figure (3b).…”

Section: Unified Structure For Data Processing and Controlmentioning

confidence: 99%

“…A control signal namely, controller/filter, is provided in the structure for selecting the input data either for control applications or for signal processing applications. When this control signal is LOW the structure effectively works as the one proposed in Figure (6) and when this control signal is HIGH the structure works as the one proposed in Figure (3b). Even though, efficient realization for the structure proposed in Figure (7) may be obtained, the authors have chosen the above structure to maintain simplicity in realization.…”

Section: Unified Structure For Data Processing and Controlmentioning

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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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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