Hankel Norm Performance Research Articles

Two-Dimensional Hankel Norm Performance of Roesser-Type Filters

This article introduces a novel approach to examining the unfavorable memory effects of two-dimensional (2-D) Roesser-type filters based on the 2-D Hankel norm performance. Novel analysis criteria are obtained such that the 2-D Roessertype filters associated with saturation have the guaranteed 2-D Hankel norm performance bound. These criteria can analyze the undesired effect reduction of Roesser-type filters for past horizontal and vertical excitations. Without external horizontal and vertical input signals, the 2-D asymptotic convergence of Roesser-type filters is ascertained under the proposed novel criteria. Finally, a numerical demonstration is given to verify the validity of the obtained criteria. The criteria presented in this paper for 2-D filters and those reported in our recent paper for one-dimensional (1-D) filters can provide a whole analysis framework for the undesired memory effects of filters.

Hankel norm performance of 2-D digital filters described by Roesser model with overflow arithmetic

ABSTRACT This paper is concerned with the problem of asymptotic stability with Hankel norm performance (HNP) of two-dimensional (2-D) digital filter characterised by Roesser model, where the 2-D system includes overflow nonlinearities and external interference or excitation of finite duration. The underlying nonlinearities cover the usual types of overflow arithmetic utilised in practice such as saturation, two’s complement, zeroing and triangular. To solve this problem, new sufficient criterion is proposed by employing quadratic 2-D Lyapunov function. The proposed criterion guarantees that the addressed system has 2-D HNP bound. This criterion can examine the unwanted memory effect (ME) reduction of 2-D interfered digital filters for past excitations. In the absence of external inputs, the asymptotic convergence of 2-D digital filters is established under the proposed criterion. The developed HNP criterion is in linear matrix inequality framework and, therefore, computationally tractable. In addition, the optimisation problem is formulated to obtain the minimum HNP of the 2-D interfered digital filter. To illustrate the effectiveness of the proposed criterion, a numerical example is provided. The criteria addressed in current paper can give a whole analysis framework for the unwanted MEs of filters.

Hankel Norm Model Reduction of Discrete-Time Interval Type-2 T–S Fuzzy Systems With State Delay

This article focuses on the model reduction problem of discrete-time time-delay interval type-2 Takagi-Sugeno (T–S) fuzzy systems. Compared with the type-1 T–S fuzzy system, the interval type-2 T–S fuzzy system has more advantages in expressing nonlinearity and capturing uncertainties. In addition, in order to simplify the analysis process, complex high-order systems can be approximated as low-order systems, which is called model reduction. In previous studies, there are few researches on model reduction of the interval type-2 T–S fuzzy system with time delay. Hankel norm is adopted to limit the error after model reduction. Based on Jensen's inequality, a linear matrix inequality (LMI) condition for the Hankel norm performance of the error system is obtained. A membership-function-dependent method based on piecewise linear membership functions is utilized to deal with mismatched membership functions where information of membership functions will be used for relaxing analysis results. Next, by a convex linearization design, the model reduction problem is formulated as a convex LMI feasibility/optimization condition. Numerical examples are given to verify the validity of the analysis.

Hankel-Norm-Based Model Reduction for Stochastic Discrete-Time Nonlinear Systems in Interval Type-2 T-S Fuzzy Framework.

This article is concerned with the problem of the Hankel-norm model reduction for stochastic discrete-time nonlinear systems in interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The IT2 T-S fuzzy model is an efficient model for describing uncertain nonlinear systems, and the model reduction is to simplify the high-order complex systems by reducing the order of the original system. The aim of this article is to reduce the order of the original stochastic discrete-time IT2 fuzzy system into lower order system without ignoring the influence of IT2 membership functions. First, the Hankel-norm performance of the stochastic discrete-time IT2 fuzzy model is analyzed. Then, based on the projection theorem and cone complementary linearization approach, a convex Hankel-norm-based model reduction approach subject to conditions in the form of linear matrix inequalities (LMIs) is obtained. A membership-functions-dependent (MFD) technique is applied to capture the information of IT2 membership functions and further reduce the conservativeness. A numerical example is presented to illustrate the effectiveness of the proposed results.

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.

Analysis of Memory Effects in Digital Filters with Overflow Arithmetic

<p>This paper deals with the problem of undesired memory effects in nonlinear digital<br />filters owing to the influence of past excitations on future outputs. The nonlinearities under consideration cover the usual types of overflow arithmetic employed in practice. Based on the Hankel norm performance, a new criterion is proposed to ensure the reduction of undesired memory effects in digital filters with overflow arithmetic. In absence of external input, the nonexistence of overflow oscillations is also confirmed by the proposed criterion. A numerical example together with simulation result showing the effectiveness of the criterion is given.</p>

Hankel Norm Performance of Digital Filters Associated With Saturation

This brief proposes a new approach to the examination and reduction of the undesired memory effect of digital filters joined with saturation, which is known as system ringing. A new criterion is established to ascertain the Hankel norm performance of digital filters joined with saturation. Using this criterion, it is possible to check the reduction of undesired responses of the filters to past excitations. The asymptotic stability for the digital filters is ensured without external input under the proposed criterion. Three improved criteria for the Hankel norm performance of digital filters are also presented based on the diagonally dominant matrix approach. A numerical simulation shows the usefulness of the developed method.

Model Approximation for Fuzzy Switched Systems With Stochastic Perturbation

In this paper, the model approximation problem is investigated for a Takagi–Sugeno fuzzy switched system with stochastic disturbance. For a high-order considered system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with a Hankel-norm performance but translates it into a lower dimensional fuzzy switched system as well. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the mean-square exponential stability with a Hankel-norm error performance for the error system. The model approximation is then converted into a convex optimization problem by using a linearization procedure. Finally, simulations are provided to illustrate the effectiveness of the proposed theory.

A novel approach to output feedback control of fuzzy stochastic systems

This paper investigates the problem of Hankel-norm output feedback controller design for a class of T–S fuzzy stochastic systems. The full-order output feedback controller design technique with the Hankel-norm performance is proposed by the fuzzy-basis-dependent Lyapunov function approach and the conversion on the Hankel-norm controller parameters. Sufficient conditions are established to design the controllers such that the resulting closed-loop system is stochastically stable and satisfies a prescribed performance. The desired output feedback controller can be obtained by solving a convex optimization problem, which can be efficiently solved by standard numerical algorithms. Finally, a Henon map system is used to illustrate the effectiveness of the proposed techniques.

T-S Fuzzy Model-Based Approximation and Filter Design for Stochastic Time-Delay Systems with Hankel Norm Criterion

This paper investigates the Hankel norm filter design problem for stochastic time-delay systems, which are represented by Takagi-Sugeno (T-S) fuzzy model. Motivated by the parallel distributed compensation (PDC) technique, a novel filtering error system is established. The objective is to design a suitable filter that guarantees the corresponding filtering error system to be mean-square asymptotically stable and to have a specified Hankel norm performance levelγ. Based on the Lyapunov stability theory and the Itô differential rule, the Hankel norm criterion is first established by adopting the integral inequality method, which can make some useful efforts in reducing conservativeness. The Hankel norm filtering problem is casted into a convex optimization problem with a convex linearization approach, which expresses all the conditions for the existence of admissible Hankel norm filter as standard linear matrix inequalities (LMIs). The effectiveness of the proposed method is demonstrated via a numerical example.

Hankel norm model approximation of Takagi–Sugeno fuzzy time-delay systems

This paper is concerned with the Hankel norm model approximation for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time delay. For a given stable T–S fuzzy system, our attention is focused on the construction of a reduced-order model which not only approximates the original system well with a Hankel norm performance but is also translated into a lower-dimensional system. By employing the modified delay partitioning method, a delay-dependent sufficient condition is developed for the asymptotic stability with a Hankel norm error performance for the error system. Then, the Hankel norm approximation problem is solved by employing the convex linearization approach, which casts the reduced-order model construction into a convex optimization problem subject to linear matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the proposed methods.

Hankel-norm model approximation for LPV systems with parameter-varying time delays

This article is concerned with Hankel-norm model approximation (HNMA) for linear parameter-varying systems with parameter-varying time delays. For a given stable system, our attention is focussed on the construction of reduced-order models, which approximate the original system well in a Hankel-norm sense. By applying the slack matrix approach, a delay-dependent sufficient condition is proposed for the robustly asymptotic stability with a Hankel-norm error performance for the error system. Then, the HNMA problem is solved by using the projection approach, which casts the model approximation into a sequential minimisation problem subject to linear matrix inequality constraints by employing the cone complementary linearisation algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the proposed methods.