Saturation Arithmetic Research Articles

Discrete-time state delayed systems with saturation arithmetic: overflow oscillation-free realization

ABSTRACT In many smart systems, such as cloud computing, networked control, manufacturing, and telecommunication, the effects of time delays are unavoidable. Saturation nonlinearity is common in many smart systems (e.g. electric systems with limited actuator power supplies, mechanical systems with position and speed constraints, fixed-point digital filters, etc.). Therefore, the study of stability of discrete-time systems (DTSs) with time delay and saturation is of high importance in practice. The global asymptotic stability (GAS) problem of such systems is investigated in this paper. The saturation nonlinearity is constrained by a convex hull with a free matrix whose infinity norm is smaller than or equal to unity. A new Lyapunov-based GAS criterion for DTSs with time-varying delay and state saturation is established. The GAS problem for DTSs with constant delay and saturation is also discussed. The obtained results can be used to ensure the absence of overflow oscillations in the considered system. In comparison to several existing criteria, the approach yields improved stability results. An example is provided to demonstrate the importance of the presented results.

Novel Stability Criterion for 2-D Digital Filters With Saturation Arithmetic

Novel Stability Criterion for 2-D Digital Filters With Saturation Arithmetic

A linear matrix inequality-based criterion for realizing externally interfered discrete system using saturation arithmetic

The article deals with stability analysis of externally interfered discrete systems with overflow nonlinearities. The proposed criterion uses passivity property to ensure the exponential stability of discrete systems in presence of saturation overflow nonlinearity. The established condition not only provides the convergence rate of the discrete system but also mitigates the influence of external disturbance on the system. It is shown that the system with saturation nonlinearities exhibits passive behaviour under external disturbance and is exponentially stable when the disturbance vanishes. The established criterion guarantees the discrete system employing saturation arithmetic to be free of limit-cycle overflow oscillations. The conditions reported are implemented in linear matrix inequality terms and are quite novel in comparison with previous works. The usefulness of the proposed approach is validated via several numerical examples.

An Optimal H∞ Approach for Local Stability Analysis of Non Linear Digital Systems with Saturation Non Linearity and External Interference

An optimal [Formula: see text] criterion for the stability investigation of non linear digital filters with saturation non linearity and external interference is proposed in this paper. The proposed criterion can be used for overflow oscillation-free realization of the non linear digital system implemented with fixed wordlength machines like digital computers or special purpose embedded systems. The proposed approach ascertains the local asymptotic stability of non linear digital filtering schemes without external interference. Further, by employing [Formula: see text] performance criterion the conditions for local stability and performance measurement are proposed with external interference. In the proposed work, the stability conditions are proposed in linear matrix inequality (LMI) by exploiting energy-based Lyapunov theory, Lipschitz inequality, and saturation arithmetic. The proposed criterion is shown to be less conservative which will improve the operating region and obtain a better estimate of [Formula: see text] performance index compared to the existing local criterion. Moreover, the proposed criterion can be used in selecting the appropriate wordlength of a digital system for tolerable values of interference energy, [Formula: see text] performance level, and fixed-point resolution. This will be an additional advantage of this work compared with existing global criteria. Sufficient examples to show the efficacy of the proposed technique are also provided.

Novel Results for Markov Jump 2D Interfered Digital Filters with State-Delay and Saturation Nonlinearities

Existing results on [Formula: see text] stability analysis problems for 2D digital filters are limited to external interference and saturation arithmetic. Unfortunately, developed results so far are not sufficient to tackle Markovian jumping parameters (MJPs) and state-delay. Such stability problem for 2D digital filters under MJPs, saturation arithmetic, state-delay and external interference has not been considered in the existing literature. In this paper, novel [Formula: see text] performance analysis criterion is first proposed for 2D interfered digital filters in which state-delay, saturation nonlinearities and MJPs are considered. The mathematical model of the underlying 2D system is described by the Roesser model. Furthermore, improved [Formula: see text] performance analysis criterion over the existing result is also obtained for 2D interfered digital filters with saturation nonlinearities only. At the end, two examples are employed to illustrate the effectiveness of the devised stability results.

Novel Realizability Criterion for Saturation Overflow Oscillation-Free 2-D Digital Filters Based on the Fornasini-Marchesini Second Model

The problem of global asymptotic stability (GAS) of two-dimensional (2-D) digital filters based on the Fornasini-Marchesini second local state-space (FMSLSS) model with saturation arithmetic is studied in this paper. A novel GAS criterion for the 2-D digital filter is presented. The obtained criterion is compared with several previously reported criteria.

Stability of Digital Filters with State-Delay and External Interference

This work addresses stability of interfered digital filters with state-delay and saturation arithmetic. By utilizing a quadratic Lyapunov functional and properties of saturation overflow, a new condition is established to ensure stability of interfered digital filters under the influence of saturation arithmetic and state-delay. The criterion is capable of finding minimum $$H_\infty $$ norm in the existence of external disturbance and ensures exponential stability in the nonexistence of disturbance. Further, an improved condition is obtained to ensure asymptotic stability of digital filters with saturation arithmetic. The established conditions are in linear matrix inequality framework and therefore computationally less demanding. It is shown that the stability criteria presented in this study are less stringent than few existing stability results. With the help of numerical examples, superiority of the presented approach is demonstrated.

Efficient Implementation of Stochastic Computing Based Deep Neural Network on Low Cost Hardware with Saturation Arithmetic

This study presents an efficient and rapid implementation of Stochastic Computing (SC) based Deep Neural Network (DNN) on a low-cost hardware platform. The proposed technique uses bipolar signal encoding in stochastic computing which relatively gives low hardware footprint compared to binary computing. Thereinafter, stochastic max function is presented and subsequently used to approximate the hyperbolic tangent activation function in SC. In addition, saturation arithmetic is proposed to reduce down scaling parameters that can further affect precision in computation. In this study, we demonstrate our SC-based DNN feasibility through a hardware accelerator prototype with the AXI Stream interface on a PYNQ Z2 board which is equipped with a XILINX ZYNQ XC7Z020-1CLG400C. The validity of this study is demonstrated through a MNIST handwritten digit recognition task. The experimental result shows our SC-based DNN model can be easily deployed on the embedded devices. The SC-based accelerator with AXI Stream interface performs at 1.877 GOP/s processing throughput, achieves higher accuracy with minimum area and energy consumption, consuming only 0.61 mm2 area and 1.89W power.

Stability of digital filters subject to external interference and state-delay

This paper presents passivity-based results to address stability of interfered digital filters with state-delay and saturation nonlinearities. A very-strict passivity condition is proposed for the digital filters by using an appropriate Lyapunov-Krasovskii functional. The established criterion ensures limit-cycle free realization of state-delayed interfered digital filters using saturation arithmetic. Conditions for passivity, input-strict passivity and output-strict passivity of the digital filters are obtained as special cases of the proposed result. In addition, an asymptotic stability condition for the digital filters with zero external interference is presented. It is also demonstrated that a stability condition reported in a recent work may be recovered from the established criterion. Numerical simulations are given to demonstrate worthiness of the proposed results.

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.

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.

Criterion for realizing state-delayed digital filters subjected to external interference employing saturation arithmetic

The problem of exponential stability and the $${\user2{H}}_{\infty }$$ performance criterion for externally disturbed state-delayed digital filter employing fixed point arithmetic in the existence of saturation arithmetic is highlighted in this paper. A limit-cycle free condition for a class of state-delayed digital filter in the existence of external disturbance and saturation arithmetic is brought out by employing Lyapunov function. The presented result ensures the exponential stability and scales down the consequences of external disturbances to the $${\user2{H}}_{\infty }$$ performance index. A numerical example simulated using MATLAB linear matrix inequality control toolbox is provided to validate effectiveness of the achieved criterion.

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.

Toward Local Stability Analysis of Externally Interfered Digital Filters Under Overflow Nonlinearity

This brief focuses on the local stability analysis of 1-D digital filters that are subject to the saturation overflow nonlinearity and external interference by exploiting local saturation arithmetic. A novel stability criterion that analyzes the local asymptotic stability of a digital filter under zero external interference is investigated. Furthermore, an extension to attain a local ${H}_{\infty}$ performance is developed to tackle the external interference. The conventional global stability criteria using the global saturation arithmetic can be derived as specific cases of the proposed local results. The proposed local stability criteria provide a lesser conservative estimate of interference attenuation level in comparison with existing global techniques. Furthermore, information on the tolerable energy bound on external interference for a given attenuation level is also revealed contrary to global schemes. In addition to this, the proposed methodology can be applied to evaluate the minimum word length to achieve the desired fixed-point resolution and the performance specifications for the sake of hardware optimization. A novel two-step approach is also provided for solving the filter stability analysis condition using convex routines. A numerical example is presented to demonstrate these features.

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>

L∞-gain performance analysis for two-dimensional Roesser systems with persistent bounded disturbance and saturation nonlinearity

The l∞-gain approach has been an essential tool in one-dimensional system theory. However, limited results have been presented in the literature for the two-dimensional (2-D) l∞-gain approach. This paper investigates the l∞-gain performance for 2-D systems in the Roesser model with persistent bounded disturbance input and saturation nonlinearity. A linear matrix inequality (LMI)-based condition is established to reduce the effect of persistent bounded disturbance input on 2-D systems within a given disturbance attenuation level based on the discrete Jensen inequality, lower bounds lemma, and diagonally dominant matrices. We apply the obtained results to the l∞-gain performance analysis for 2-D digital filters with saturation arithmetic.

Asymptotic Stability of Fixed-Point State-Space Digital Filters with Saturation Arithmetic and External Disturbance: An IOSS Approach

A criterion for the input/output-to-state stability of interfered state-space digital filters with saturation arithmetic and external interference is presented. The proposed linear matrix inequality-based criterion ensures the reduction in the effect of external interference as well as confirms the asymptotic stability in the absence of external interference. The criterion turns out to be an improvement over a previously reported criterion. A numerical example is given to illustrate the applicability of the proposed criterion.

A new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with interference

Stability criteria have been proposed previously by Ahn for two-dimensional (2-D) digital filters described by the Roesser model with external interference. However, no stability criteria have yet been established for 2-D digital filters described by the Fornasini–Marchesini second model. In this paper, we propose a new realization criterion for 2-D digital filters in the Fornasini–Marchesini second model with saturation arithmetic and external interference. This new criterion guarantees that 2-D digital filters in this model are asymptotically stable with a guaranteed H∞ performance. The criterion is described by linear matrix inequalities (LMIs). Illustrative examples show the effectiveness of the proposed new criterion.

Stability of Discrete-Time Switched Linear Systems with Saturation Arithmetic

This paper addresses a strategy for the stability of discrete-time switched linear systems with saturation arithmetic. It is of closed-loop nature and is designed from the solution of what we called Lyapunov-Metzler inequalities from which the stability condition is expressed. The theoretical results are illustrated by means of examples.