New results on saturation overflow stability of 2-D state-space digital filters described by the Fornasini–Marchesini second model

Agarwal, Nipun; Kar, Haranath

doi:10.1016/j.sigpro.2016.05.022

Cited by 17 publications

(7 citation statements)

References 55 publications

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“…Among 2D systems, the design procedure for l 2 − l ∞ filter is mainly discussed based on the systems with state delays and saturation in [12]. The saturation problem is most common in practical systems with typical nonlinear properties, and a large number of 2D systems have been studied for this problem [13]- [16]. In [17], [18] for both continuous and discrete 2D systems researchers devoted to H ∞ filtering problem under the uncertain systems.…”

Section: Introductionmentioning

confidence: 99%

Iterative Learning Control Design of Switched Systems With Markovian Jump Parameters via Fuzzy Approach

Wang

2019

IEEE Access

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In this paper, based on Takagi-Sugeno (T-S) approach the work is concerned with the iterative learning control (ILC) problem for a class of switched systems with data packet dropouts. The designed scheme is described by a class of Markovian switching systems with transition probabilities which are time-variant in a network environment. The links of network communications between controllerto-actuator (C/A) and sensor-to-controller (S/C) are unreliable. In terms of the construction of twodimensional (2D) T-S model, a novel composite strategy of 2D fuzzy iterative learning output feedback control is proposed. The sufficient conditions on stochastic stability are obtained by the 2D Lyapunov stability theory. Furthermore, the dynamics of the closed-loop are guaranteed to be stochastically stable and the desired H ∞ performance is also provided. The solutions of the ILC controller are derived by the application of the cone complementarity linearisation (CCL) procedure. Finally, a numerical simulation is illustrated to show the validity of the design. INDEX TERMS Iterative learning control, Markovian jump systems, Takagi-Sugeno fuzzy, data packet dropout, time variant.

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Section: Introductionmentioning

confidence: 99%

Iterative Learning Control Design of Switched Systems With Markovian Jump Parameters via Fuzzy Approach

Wang

2019

IEEE Access

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“…Note that most LMI conditions in [11], [12], [21], [22] are only sufficient and far from necessity. These methods use Lyapunov functions of restricted form [21] and thus satisfactory results have not been obtained on the exactness of the resulting LMI-based conditions [18].…”

Section: Introductionmentioning

confidence: 99%

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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“…Thus, the formulation of overflow stability criteria for digital filters is an important research problem. The stability analysis of digital filters with saturation arithmetic has been a subject of extensive research (Agarwal and Kar, 2016a, 2016b; Ahn, 2013, 2014; Ahn and Kar, 2015; Ahn et al , 2016; Amjad et al , 2017; Arif et al , 2017; Kar, 2007, 2010; Kar and Singh, 1998, 2003, 2004, 2005; Kokil and Shinde, 2015a, 2015b; Kokil et al , 2018; Li and Zheng, 2012; Liu and Michel, 1992, 1996; Ooba, 2003, 2010, 2013; Rehan et al , 2016; Ritzerfeld, 1989; Shen et al , 2012; Singh, 1985, 1990, 2006).…”

Section: Introductionmentioning

confidence: 99%

Overflow oscillation-free realization of digital filters with saturation

Agarwal

Kar

2018

COMPEL

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Purpose The purpose of this paper is to establish a criterion for the global asymptotic stability of fixed-point state–space digital filters using saturation overflow arithmetic. Design/methodology/approach The method of stability analysis used in this paper is the second method of Lyapunov. The approach in this paper makes use of a precise upper bound of the state vector of the system and a novel passivity property associated with the saturation nonlinearities. Findings The presented criterion leads to an enhanced stability region in the parameter-space as compared to several existing criteria. Practical implications When dealing with the design of fixed-point state–space digital filters, it is desirable to have a criterion for selecting the filter coefficients so that the designed filter becomes free of overflow oscillations. The criterion presented in this paper provides enhanced saturation overflow stability region and therefore facilitates the designer greater flexibility in selecting filter parameters for overflow oscillation-free realization of digital filters. Originality/value The approach uses the structural properties of the saturation nonlinearities in a greater detail. The exploitation of upper bound of the system state vector together with a new passivity property of saturation nonlinearities is a unique feature of the present approach. The presented approach may lead to results not covered by several existing approaches.

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New results on saturation overflow stability of 2-D state-space digital filters described by the Fornasini–Marchesini second model

Cited by 17 publications

References 55 publications

Iterative Learning Control Design of Switched Systems With Markovian Jump Parameters via Fuzzy Approach

Iterative Learning Control Design of Switched Systems With Markovian Jump Parameters via Fuzzy Approach

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

Overflow oscillation-free realization of digital filters with saturation

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