Aryan Saadat Mehr

On

In this paper, we present a new design method for the H∞ filtering of discrete-time Takagi-Sugeno (TS) fuzzy systems. The parameters of the filter are assumed to be linearly dependent on the normalized fuzzy weighting functions. By using an augmentation technique, the design parameters are incorporated into a filtering error system. In order to derive less-conservative results and reduce the filtering error, a new condition is established to ensure the H∞ performance of the filtering error system. By introducing more slack matrices, the solution set of the filter parameters is extended. By using a partitioning technique, a design method for the H∞ filter is proposed in terms of linear matrix inequalities (LMIs). An example demonstrates the improvement of the proposed design method over an existing approach.

{\cal H}_{\infty }

This paper investigates the problem of energy-to-peak filtering for both discrete-time and continuous-time systems with polyhedral uncertainties in the state-space equations. By increasing the flexible dimensions in the solution space for the energy-to-peak optimization, less conservative results on the robust energy-to-peak filtering are obtained. The filter parameters can be readily designed by solving a set of parameter-dependent linear matrix inequalities (LMIs). In comparison with the existing methods, the improvement of the proposed method over the existing results is shown via two numerical examples.

Filtering for Discrete-Time Takagi–Sugeno Fuzzy Systems

The optimal design of finite impulse response (FIR) filters for equalization/deconvolution is investigated in this paper. Two practical yet challenging constraints are incorporated into the modeling of the equalization system: (1) The parameters of the communication channel model are arbitrarily time-varying within a polytope with finite known vertices; (2) at the received end, the received signal is usually intermittent due to network-induced packet dropouts which are modeled by a stochastic Bernoulli distribution. Under the stochastic theory framework, a robust design method for the FIR equalizer is proposed such that the equalization system can achieve the prescribed energy-to-peak performance even it is subject to uncertainties, external noise, and data missing. Sufficient conditions for the existence of the equalizer are derived by a set of linear matrix inequalities (LMIs). An illustrative design example demonstrates the design procedure and the effectiveness of the proposed method.

Improved robust energy-to-peak filtering for uncertain linear systems

The linear switched time-varying (LSTV), polyphase (blocked), and alias-component representations of linear periodically time-varying (LPTV) systems are studied. In particular, alias-components are related to the time-shifted versions of the system. It is shown that in general, a filterbank is equivalent to the cascade connection of two LPTV systems. By generalizing some of the results of the LSTV representation of LPTV systems, it is shown that for relatively coprime integers p and m, a p-channel filterbank that has LPTV filters with period m is equivalent to an mp-channel filterbank with LTI filters. The representation of multirate systems that have LPTV kernels is discussed next. Due to the presence of the upsampler and downsampler, there are some degrees of freedom in the choice of the kernel. This redundancy is dealt with by choosing from various subclasses so that there is a one-to-one relationship between a multirate system and its kernel. Then, we find the LPTV kernel that has the least period.

Robust FIR equalization for time-varying communication channels with intermittent observations via an LMI approach

This paper studies the statistical behavior of the normalized subband adaptive filtering (NSAF) algorithm. An accurate statistical model of the NSAF algorithm is obtained. In the derivation, we focus on Gaussian correlated input signals. By assuming that the analysis filter bank is paraunitary and taking into account the full band adaptation mechanism of the NSAF, expressions for the first and the second moments of the adaptive filter weights are derived without invoking the slow adaptation assumption. In the derivations, several hyperelliptic integrals appear. To tackle those integrals induced by Gaussian correlated inputs, we first give a solution by resorting to the adaptive Lobatto quadrature. By invoking the averaging principle, two other approximation methods, the chi-square method and the partial fraction expansion method, are presented to approximate the statistical model as well. Monte Carlo (MC) simulation results corroborate our predictions. The Lobatto quadrature method achieves a good agreement with the MC simulation results, even for a relatively large step size. Compared with the chi-square method and the partial fraction expansion method, the Lobatto quadrature method gives better performance in terms of predicting the mean square error when the length of the adaptive filters is small to medium. The chi-square approximation method and the partial fraction expansion method give a satisfactory performance with a relatively low computational complexity when the filter length is large.

Representations of linear periodically time-varying and multirate systems

The affine projection algorithm (APA) is a generalization of the normalized least mean square algorithm. We propose a variable regularization factor for the APA. Instead of the conventional assumption that the a posteriori error is zero, we incorporate the statistical characteristic of the noise into the adaptation process based on a system identification setup. Exact and approximate formulations for the optimal regularization factor are derived. Numerical simulation results show that the proposed algorithm improves the performance of the APA in terms of its convergence rate and steady-state misalignment.

Stochastic Analysis of the Normalized Subband Adaptive Filter Algorithm

We first use the Fourier series to find the steady-state response of discrete-time linear periodically time-varying (LPTV) systems to periodic inputs. Then, in order to obtain the response of LPTV systems to general inputs, we use the Fourier transform (FT) and establish a direct link between alias-component matrices and LPTV systems modeled by periodically time varying difference equations. This is given in terms of the Fourier series of the parameters in the model.

A Variable Regularization Method for Affine Projection Algorithm

We derive a new method for the identification of discrete linear periodically time-varying (LPTV) systems. Take an LPTV system with period M, and assume that an input with period N is applied to this system, where N is a multiple of M. The output of this system will be periodic with period N. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. We show that the method achieves the Cramer-Rao lower bound (CRLB). A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification. Simulation results illustrate the efficiency of the proposed algorithm.

On alias-component matrices of discrete-time linear periodically time-varying systems

A new method for the identification of discrete linear periodically time-varying (LPTV) systems is derived in this paper. Take an LPTV system with period M, and assume that an input with period N is applied to this system, where N is a multiple of M. The output of this system will be periodic with period N. Using such periodic inputs, we show that the problem of identification of LPTV systems can be formulated in the frequency domain. By using the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. Simulation results illustrate the efficiency of the proposed algorithm.

Identification of LPTV systems in the frequency domain

We consider a multirate system, which is a generalization of linear time-invariant systems. Such a system is invariant to a certain shift in the input sequence. In particular, assume that p and q are coprime. A multirate system with the property that a delay of mq samples in its input sequence results in a delay of mp samples in its output sequence is called an (mp, mq)-periodic system. This multirate system can be obtained by cascading an upsampler, followed by a linear periodically time-varying (LPTV) kernel system, then followed by a downsampler. Here, we study the alias-component matrices of multirate systems. We show that they can be obtained from the alias-component matrices of their LPTV kernels by some row and column additions. An example shows the use of the method to design rate changers for a specified frequency band swap.