Generalized Overflow Nonlinearities Research Articles

New Stability Results for 2-D Digital Filters With Generalized Overflow Nonlinearities

New Stability Results for 2-D Digital Filters With Generalized Overflow Nonlinearities

Stability of Discrete-Time Delayed Systems Subject to External Interference and Generalized Overflow Nonlinearities

This article concerns the stability of delayed discrete-time systems (DTSs) through <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance under external interference and generalized overflow nonlinearities. The novel criteria that analyze the exponential stability of DTSs with constant state delays are presented. Moreover, an extension to attain the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> performance is developed to handle the external interference of systems with time-varying delays based on Wirtinger-based inequality and reciprocal convex inequality. For such systems, the presented approach ensures zero-input overflow stability as well as robustness against interferences with a guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> level. The presented methodology can also be applied to determine the minimum attenuation level to achieve the desirable performance specifications for the sake of hardware optimization. The presented criteria are less conservative than several existing criteria. The efficacy of the presented criteria is exemplified by examples.

A Passivity Based Approach for Digital Filters Subjected to External Disturbance and Nonlinearities

The aim of this work is to present a passivity based approach for stability analysis of state-space digital filters realized with fixed-point arithmetic and generalized overflow nonlinearities. The criterion ensures the digital filter is free from limit cycle oscillations subjected to overflow nonlinearities and external interference. The stability conditions of the digital filter are formulated via passivity based approach under different nonlinearities, namely, zeroing, saturation, two’s complement, and triangular. The criterion also ensures the asymptotic stability without external interference. The proposed work is in linear matrix inequality framework and hence, is computationally tractable. Sufficient numerical examples are provided in support of established results.

Stability of Uncertain 2-D Discrete Systems in Presence of Generalized Overflow Nonlinearities

Stability analysis of two-dimensional (2-D) discontinuous systems with generalized overflow nonlinear effects is considered in this work. The 2-D models considered are the well-known Fornasini Marchesini Second Local State-Space (FMSLSS) model and the Roesser model. The effect of uncertainties and interim-like variable time-delays on the system is also examined in the study. Using reciprocally convex approach we provide stability criteria which is organized as matrix inequalities. Numerical illustrations are given to demonstrate the applicability of the results.

Novel ISS criteria for digital filters using generalized overflow non-linearities and external interference

Sufficient criteria for input-to-state stability (ISS) of fixed-point state-space interfered digital filters with generalized overflow non-linearities are presented. The generalized overflow non-linearities under consideration cover the usual types of overflow arithmetic employed in practice, such as saturation, zeroing, two’s complement and triangular. The criteria not only ensure diminishing consequence of external interference but also confirm the asymptotic stability of the system when external interference disappears. The criteria are derived in the linear matrix inequality (LMI) framework. Simulation results are provided to illustrate the utility of the presented approach. With the help of one example, it is illustrated that the presented approach can lead to a less stringent ISS condition for the digital filters with saturation non-linearities compared with a previously reported approach.

Stability analysis of digital filters subjected to interference using generalized overflow nonlinearities

In this paper, we feature a new criterion using an input–output-to-state stability (IOSS) approach for digital filters employing fixed-point arithmetic with generalized overflow nonlinearities in the presence of external disturbances. The proposed linear matrix inequality (LMI)-based criterion eliminates the presence of limit cycles and ensures not only the IOSS of digital filters but also their asymptotic stability when external interference is exhausted. Through several numerical examples, the effectiveness of the proposed criterion is illustrated, and it is shown that it covers a broad class of nonlinearities, namely saturation, zeroing, two's complement, and triangular.

Novel Results for Induced l∞ Stability for Digital Filters with External Noise

This paper establishes novel criteria for the induced [Formula: see text] stability to avoid overflow oscillations in fixed-point digital filters with generalized overflow non-linearities and external noise. The proposed linear matrix inequality (LMI)-based criteria ensure exponential stability as well as confirm reduction in the influence of external noise. The generalized overflow non-linearities which are considered for analysis commonly occur in practice, viz. saturation, zeroing, two's complement, and triangular. The presented approach unifies a string of existing results which are derived by considering saturation non-linearities and external interference. Simulation examples are shown to validate the usefulness of the proposed approach.

Criterion for limit cycle-free state-space digital filters with external disturbances and generalized overflow non-linearities

This paper investigates the problem of [Formula: see text] elimination of overflow oscillations in fixed-point state-space digital filters using generalized overflow non-linearities and external disturbance. The generalized overflow non-linearities under consideration cover the common types of overflow arithmetic used in practice, for instance zeroing, two’s complement, triangular and saturation. New criteria are established to ensure not only exponential stability, but also reduction in the effect of external disturbance to an [Formula: see text] norm constraint. The obtained criteria are in linear matrix inequality (LMI) framework and, hence, are computationally tractable. The presented approach constitutes a generalization over several previously reported approaches for the [Formula: see text] elimination of overflow oscillations. For saturation non-linearities, the presented result turns out to be less conservative than several existing criteria. Numerical examples are provided to demonstrate the effectiveness of the presented approach.

$$l_2 -l_\infty $$ l 2 - l ∞ Suppression of Limit Cycles in Interfered Digital Filters with Generalized Overflow Nonlinearities

This paper is concerned with the problem of the suppression of overflow oscillations in fixed-point state-space interfered digital filters using generalized overflow nonlinearities. The proposed linear matrix inequalities-based $$l_2 -l_\infty $$l2-lź criteria not only assure asymptotic stability, but also minimize the effect of external interference to a prescribed attenuation level. The usefulness of the criteria is illustrated by numerical examples.

A Delay-Dependent Approach to Stability of Uncertain Discrete-Time State-Delayed Systems with Generalized Overflow Nonlinearities

This paper addresses the problem of global asymptotic stability of a class of uncertain discrete-time state-delayed systems employing generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. A new computationally tractable delay-dependent criterion for global asymptotic stability of such systems is presented. A numerical example is given to illustrate the effectiveness of the proposed method.

LMI‐Based Criterion for the Robust Stability of 2D Discrete State‐Delayed Systems Using Generalized Overflow Nonlinearities

This paper addresses the problem of global asymptotic stability of a class of discrete uncertain state‐delayed systems described by the Fornasini‐Marchesini second local state‐space (FMSLSS) model using generalized overflow nonlinearities. The uncertainties are assumed to be norm bounded. A computationally tractable, that is, linear‐matrix‐inequality‐(LMI‐) based new criterion for the global asymptotic stability of such system is proposed. It is demonstrated that several previously reported stability criteria for two‐dimensional (2D) systems are recovered from the presented approach as special cases. Numerical examples are given to illustrate the usefulness of the presented approach.

Robust stability of 2-D discrete systems employing generalized overflow nonlinearities: An LMI approach

This paper deals with the problem of global asymptotic stability of a class of uncertain discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model using generalized overflow nonlinearities. The systems under investigation involve parameter uncertainties that are assumed to be deterministic and norm bounded. An LMI-based criterion for the global asymptotic stability of such systems is proposed. The proposed criterion is compared with previously reported criteria.

Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities

This paper considers the problem of global asymptotic stability of a class of nonlinear uncertain discrete-time state-delayed systems. The class of systems under investigation involves multiple state delays, norm-bounded parameter uncertainties, and generalized overflow nonlinearities which cover usual types of overflow arithmetic used in practice. A new criterion for the global asymptotic stability of such systems is presented. A numerical example is given to illustrate the applicability of the criterion presented.