State-space Digital Filters Research Articles

Improved Delay-Dependent Stability Analysis of Fixed-Point State-Space Digital Filters With Time-Varying Delay and Generalized Overflow Arithmetic

This paper is concerned with the stability analysis of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. This paper aims to derive a delay and nonlinear function bound dependent asymptotical stability criterion with less conservatism. Firstly, a new Lyapunov functional with several augmented terms, including extra free matrices and overflow nonlinear function, is constructed such that it has a relaxed positive condition. Then, for bounding the summation term arising in the forward difference of Lyapunov functional, a new lemma is developed to introduce the terms for linking the delayed states and the overflow nonlinear function, the Wirtinger-based summation inequality and several zero-value terms are applied to add more cross terms. As a result, a stability criterion with less conservatism is established and its conservatism. Finally, several numerical examples are given to illustrate the advantages of the proposed method.

Realisation of overflow oscillation-free fixed-point digital filters with 2’s complement arithmetic

ABSTRACT In this paper, we focus on the problem of overflow oscillation elimination in 2’s complement state variable realisation of fixed-point digital filters. A new global asymptotic stability (GAS) criterion for the zero-input fixed-point state-space digital filters employing 2’s complement overflow arithmetic is proposed. The proposed criterion captures the structural properties of 2’s complement overflow nonlinearities in a greater detail as compared to several existing criteria. A comparative evaluation of the proposed criterion with various previously reported criteria is made. The obtained criterion turns out to be less stringent than several existing results. An example along with simulation results to substantiate the utility of the criterion is also provided.

Criterion for the H∞ Suppression of Overflow Oscillations in Fixed Point Digital Filters Employing Saturation Nonlinearities and External Interference

This paper proposes a novel criterion for suppressing the [Formula: see text] overflow oscillations in fixed point state-space digital filters employing saturation nonlinearities and external interference. The proposed criterion can be used to ensure the exponential stability (ES) and diminish the external interference effects to an [Formula: see text] norm constraint. An example is given to exemplify the utility of the obtained results.

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.

An Improved Stability Criterion for Digital Filters With Generalized Overflow Arithmetic and Time-Varying Delay

This brief concerns the stability of fixed-point state-space digital filters with generalized overflow arithmetic and a time-varying delay. A relaxed lemma that includes a commonly used lemma as a special case is developed to show the relationship between the state and the overflow arithmetic, and a Lyapunov functional with positive-definite conditions that are more relaxed than usual is constructed. As a result, a less conservative stability criterion is established, and the efficiency and merit of the criterion are illustrated with a numerical example.

Weighted Minimization of Roundoff Noise and Pole Sensitivity Subject to <i>l</i><sub>2</sub>-Scaling Constraints for State-Space Digital Filters

Weighted Minimization of Roundoff Noise and Pole Sensitivity Subject to <i>l</i><sub>2</sub>-Scaling Constraints for State-Space Digital Filters

Overflow oscillations free implementation of state-delayed digital filter with saturation arithmetic and external disturbance

This paper presents a sufficient condition for exponential stability and confirms [Formula: see text] performance of state-delayed digital filters in the simultaneous existence of saturation arithmetic and external disturbance. The realization of limit-cycle free state-space digital filters is carried out by utilizing better characterization of saturation nonlinearities. The presented criterion not only ensures exponential stability but also reduces effect of external interference to a specific attenuation level. The obtained condition is in linear matrix inequality framework, so it is easily tractable. It is also shown that many results reported in literature may be retrieved as a special case from the proposed condition. With the help of numerical examples, it is shown that the presented approach provides enhanced stability region for the digital filters as compared to an existing criterion appeared in literature.

Hankel Norm Performance of Interfered Fixed-Point State-Space Digital Filters with Quantization/Overflow Nonlinearities

This paper presents a new linear matrix inequality (LMI)-based approach for the Hankel norm performance of fixed-point state-space digital filters subjected to external interference or excitation of finite duration and operating under various concatenations of quantization and overflow nonlinearities. The approach can be used to check the attenuation of undesired memory effects of past excitations on future outputs in the digital filters and to test the asymptotic stability in the absence of external input. The convex optimization problem with LMI constraints is formulated to determine the minimum Hankel norm performance of the digital filter. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed approach.

Overflow oscillation-free realization of digital filters with saturation

PurposeThe 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/approachThe 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.FindingsThe presented criterion leads to an enhanced stability region in the parameter-space as compared to several existing criteria.Practical implicationsWhen 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/valueThe 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.

New Criterion for l2–l∞ Stability of Interfered Fixed-Point State-Space Digital Filters with Quantization/Overflow Nonlinearities

The problem of l2–l∞ stability and disturbance attenuation performance analysis of fixed-point state-space digital filters with external disturbance and finite wordlength nonlinearities is studied in this paper. The finite wordlength nonlinearities are composite nonlinearities representing concatenations of quantization and overflow correction employed in practice. Using sector-based characterization of the finite wordlength nonlinearities, a new l2–l∞ stability criterion for the reduction of the effects of external disturbance to a given level and to confirm the nonexistence of limit cycles in the absence of external interference is established. Numerical examples are given to illustrate the efficacy of the proposed criterion.

ISS Criterion for the Realization of Fixed-Point State-Space Digital Filters with Saturation Arithmetic and External Interference

This paper investigates the problem of the input-to-state stability (ISS) of fixed-point state-space digital filters in the presence of saturation overflow arithmetic and external interference. By utilizing an augmented Lyapunov function and the passivity property associated with multiple saturation nonlinearities, a new criterion for the ISS of interfered digital filters with saturation is proposed. When the external interference is present, the criterion can be used to determine ISS of digital filters. Without the external interference, the criterion is capable of detecting the asymptotic stability of digital filters. The proposed ISS criterion is in linear matrix inequality framework and, hence, is computationally tractable. The obtained criterion turns out to be less conservative than a recently reported ISS criterion. The superiority of the presented approach over the existing techniques is confirmed by numerical examples.

New passivity results for the realization of interfered digital filters utilizing saturation overflow nonlinearities

This paper considers the passivity performance analysis of fixed-point state-space digital filters with saturation nonlinearities in the presence of external interference. The purpose is to establish new stability criteria in terms of linear matrix inequality (LMI) such that fixed-point state-space digital filters with saturation nonlinearities in the existence of external interference ensure passivity performance with its storage function. The presented results not only ensure state strict and input state strict passivity in the presence of external interference but also confirm asymptotic stability without external interference. The obtained conditions for fixed-point state-space digital filters are based on passivity properties and, hence, are quite novel to previously proposed criteria. Finally, simulation results are given to demonstrate the effectiveness of the proposed work.

New realizability criterion for digital filters with external disturbance and saturation arithmetic

An improved stability criterion for fixed-point state-space digital filters in the occurrence of external disturbance and saturation nonlinearities by using induced l∞ approach is presented. The realization of state-space digital filters which is free from limit-cycles is brought out by utilizing a better characterization of the saturation nonlinearities and free-weighting matrices. The proposed criterion promises exponential stability and also diminishes the influence of external disturbance to a prescribed induced l∞ norm constraint. The superiority of the suggested method for filter design is exemplified by means of numerical examples.

Passivity Based Stability Condition for Interefered Digital Filters

This paper presents a new passivity condition for fixed-point state-space interfered digital filters using saturation arithmetic. Passivity is a way to characterize input-output stability of a system, that is, supplied bounded input energy produces bounded output energy. The presented criterion also ensures asymptotic stability of the state-space digital filter with zero external disturbances. The result is expressed in terms of linear matrix inequality, and therefore, can be solved via existing numerical packages. A numerical example is arranged to validate the usefulness of the proposed method.

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.

A New Realizability Condition for Fixed-Point State-Space Interfered Digital Filters Using Any Combination of Overflow and Quantization Nonlinearities

A linear matrix inequality-based new criterion for the input-to-state stability of fixed-point state-space digital filters in the presence of quantization/overflow nonlinearities and external interference is presented. The presented criterion ensures the reduction in the effect of external interference as well as guarantees the asymptotic stability of digital filters without external interference. Some examples highlighting the effectiveness of the presented approach are provided.

Variable state-space digital filters using series approximations

This paper proposes new state-space formulations of IIR Variable Digital Filters (VDFs) based on frequency transformations. The existing frequency transformation-based state-space VDFs require restrictions on the transfer functions, state-space representations, and tuning characteristics. On the other hand, the proposed method is free from such restrictions. We achieve this goal by applying series approximations to the conventional state-space formulations of frequency transformations. This approach also allows us to realize the proposed VDFs without complicated computations such as the inverse matrix and the square root. Furthermore, the proposed VDFs show high accuracy with respect to the finite wordlength effects as well as the approximation errors.

An Improved Criterion for Induced Stability of Fixed-Point Digital Filters with Saturation Arithmetic

<p>This paper establishes a criterion for the induced stability of fixed-point state-space digital filters with saturation nonlinearities and external interference. The criterion is established in a linear matrix inequality (LMI) setting, and therefore, computationally tractable. The criterion turns out to be an improvement over a previously reported criterion. A comparison of the presented criterion with existing criterion is made. Numerical examples are given to demonstrate the usefulness of the proposed approach.</p>

New results on saturation overflow stability of 2-D state-space digital filters

This paper establishes a novel criterion for the global asymptotic stability of two-dimensional fixed-point state-space digital filters described by Roesser model with saturation nonlinearities. The criterion makes use of a precise upper bound of the system state vector together with a novel passivity property associated with the saturation nonlinearities. The criterion is presented in a linear matrix inequality (LMI) setting, and hence, computationally tractable. A comparison of the presented criterion with several existing criteria is made.

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

In this paper, the problem of global asymptotic stability of two-dimensional fixed-point state-space digital filters described by the Fornasini–Marchesini second local state-space model with saturation nonlinearities has been investigated. By making use of a precise upper bound of the system state vector and a novel passivity property associated with the saturation nonlinearities, a new sufficient global asymptotic stability criterion has been proposed. Presented criterion has been compared with several existing criteria. An illustrative example is given to demonstrate the efficacy of the proposed method.