Transmission matrix of a class of discrete-time systems

Some new properties of the transmission matrix of the class of scalar, linear, discrete-time-varying systems, of order m, which are totally m-controllable and totally m-observable, are found. The results can be applied to the design, in the time domain, of discrete-time-varying or time-invariant systems.     

一类离散切换系统的性能分析

针对一类含有不确定性和时滞的离散切换系统,探讨了H∞性能分析问题。假设所考虑的线性不确定性具有线性分式形式,综合利用Lyapunov-Krasovskii函数和Finsler’s引理,给出判断系统满足H∞性能界γ的充分条件,并且γ的上界可以通过求解一组线性矩阵不等式获得。最后通过一个数值算例说明方法的有效性。     

Optimum Laguerre networks for a class of discrete-time systems

An analytical approach is introduced that directly yields the optimum value of the Laguerre parameter b. This is achieved by minimizing the mean-square error between the unit-sample response of the given discrete system and that of its Laguerre counterpart. It is shown that Laguerre networks are best suited to realized systems whose exponential unit-sample responses die down rapidly     

Stability analysis for a class of discrete-time two-dimensional nonlinear systems

Stability analysis for a class of discrete-time two-dimensional nonlinear systems is addressed in this paper. A linear matrix inequality based sufficient condition for asymptotic stability is proposed. This condition is an analogous counterpart for two-dimensional linear systems which is shown to be easily verifiable and suitable for design problems. The result is illustrated by a numerical example.     

A time-frequency distribution of Cohen's class with a compoundkernel and its application to speech signal processing

Time-frequency distributions belonging to Cohen's class have been discussed in deterministic nonstationary signal processing. The Wigner-Ville distribution is the first to be proposed among the class and is most widely studied and applied in the various fields. However, one of the main difficulties with the Wigner-Ville distribution is that it indicates spurious values in the intensity due to interference particularly prevalent for multicomponent signals. The authors propose a new type kernel function that is the product of the Choi-Williams kernel and the Margenau-Hill kernel. Specific types of signals: sinusoidal signals, chirp signals, and others are analyzed using the new distribution in comparison with the results by the Wigner-Ville and the Choi-Williams distributions. The present distribution does not indicate spurious intensity in the regions where the other two distributions do. In the authors' distribution, the spurious values are transferred to places where one would expect the signal's inherent intensity at least for a signal of pure sine waves. Thus correct values of the signal's intensity are slightly modulated due to cross talk. The three distributions are also compared numerically for these signals and for speech signals to show the advantages of the present distribution     

Global robust stability of a class of discrete-time interval neural networks

This paper is concerned with global robust stability of a general class of discrete-time interval neural networks which contain time-invariant uncertain parameters with their values being unknown but bounded in given compact sets. We first introduce the concept of diagonally constrained interval neural networks and present a necessary and sufficient condition for global robust stability of the interval networks regardless of the bounds of nondiagonal uncertain parameters of state feedback and connection weight matrices. Then we extend the result to general interval neural networks. Finally, simulation results illustrate the characteristics of the main results.     

On the Wold decomposition of discrete-time cyclostationaryprocesses

The Wold decomposition of discrete-time CS (cyclostationary) processes into a regular and predictable component is considered. Using the properties of the zeros of linear periodic systems, it is shown that the predictable component consists of a linear combination of sine waves     

Sufficient conditions for alias-free direction of arrivalestimation in periodic spatial spectra

The problem of broadband spatial spectral estimation with a uniform linear array where the interelement spacing is greater than a half-wavelength over the frequency band of interest is addressed. It is shown that by using properly chosen frequencies, ambiguities in the source location estimates can be resolved. The proposed approach is based on the selection of the wavelengths to ensure that aliased versions of the source component occur at different angles, while the source component in the true direction occurs at the same angle at different frequencies     

On the zeros of discrete-time linear periodic systems

Discrete-time linear periodic single-input/single-output (SISO) systems having uniform relative degree are considered. A closed-form expression of the blocking input is derived and exploited to obtain a computationally advantageous characterization of the structural zeros. Indeed, it suffices to compute the eigenvalues of a suitably defined (n × n) matrix, wheren is the system order. It is shown that, in contrast to the general case studied in previous papers, the number of zeros of linear periodic SISO systems with uniform relative degree is always time invariant and equal to the difference between the system order and the relative degree. The new characterization is also used to provide a simple expression for the zeros of linear periodic systems described by input-output difference equations.This paper has been partially supported by MURST Project Model Identification, System Control, Signal Processing.     

Frequency condition for the stochastic stability of a class of discrete-time control systems

This letter concerns the nonlinear discrete closed-loop control system with a randomly time-varying parameter. For such a system, a frequency criterion of asymptotic stochastic stability in mean square is presented. A simple example is included for illustration.     

On positive—Real discrete-time transfer functions

An algebraic formulation of the positive-real (PR) condition of transfer functions is given. It provides a simple interpretation in terms of a polynomial inequality whose computational solution may be shown to be numerically stable. A class of transfer functions which do not verify the PR condition is given in terms of the roots of these polynomials. An example of interest in adaptive control theory furnishes insight into the proposed method.     

On the cascade of incoherent discrete-time microwave photonic filters

In this study, a theoretical analysis leading to the derivation of the overall incoherent transfer function of a microwave photonic filter composed of the cascade of two optical structures is developed. Two cases that are more common in practice are considered, i.e., 1) a filter illuminated by a single optical source and 2) a compound filter illuminated by an optical source array. In both cases, the conditions on which the overall incoherent transfer function can be expressed as the product of the individual incoherent transfer functions of each of the optical structures that compose the filter are investigated. In other words, the conditions where the end-to-end electrical linearity is preserved when cascading incoherent optical structures are studied. These results are of importance for the design of complex incoherent filter structures aiming to provide high Q or single resonance performance.     

Convergence analysis of alias-free subband adaptive filters based on a frequency domain technique

Convergence analysis of alias-free subband adaptive filters (SADFs) is presented based on a frequency-domain technique where instead of analyzing the adaptive algorithms in the time-domain, the averaging method and the ordinary differential equation (ODE) method are applied to the frequency-domain expressions of the adaptive algorithms converted by the discrete Fourier transform. As an alias-free SADF algorithm, the SADF proposed by Pradhan and Reddy is known. In this paper, this technique is first applied to the Pradhan's SADF. The stability of the Pradhan's SADF is verified in the frequency domain, and a simple formula to evaluate the mean square error (MSE) of the algorithm is theoretically derived. By using a slight modification, the technique can be applied to the two-band delayless subband adaptive filter (DLSADF) with the Hadamard transform. The stability condition and the MSE of the DLSADF with the Hadamard transform are also obtained. Simulation results of both algorithms show the validity of the theoretical results.     

On the uniform approximation of discrete-time systems bygeneralized Fourier series

In this paper, model sets for linear time-invariant discrete-time systems spanned by fixed orthonormal bases are studied. It is shown that the Fourier series of the system transfer function with respect to these bases converges uniformly on the unit circle if the frequency response of the system is Dini-Lipschitz continuous     

On Hautus-type conditions for controllability of implicit linear discrete-time systems

Four notions of controllability for general (i.e., possibly nonregular) implicit linear discrete-time systems are considered. Relationships between them are studied. A Hautus-type characterization of all of these notions is also given.This work was performed under the auspices of RP.I.02: Teoria sterowania i optymalizacji ciagych ukadów dynamicznych i procesów dyskretnych.     

On the design of nonlinear discrete-time predictors (Corresp.)

The problem of minimum mean-squared error prediction of a discrete-time random process using a nonlinear filter consisting of a zero-memory nonlinearity followed by a linear filter is studied. Classes of random processes for which the best predictor is realizable using a nonlinear filter of the above form are discussed. For those random processes for which the best predictor is not realizable using the above nonlinear filter, an iterative procedure is presented for finding a suboptimal nonlinear filter; special attention is directed to the case where the nonlinearity is a polynomial. Also, a noniterative approach based on nonlinear regression is presented.     

Deadbeat control of discrete-time systems incorporating deadbeat discrete-time observers

A simple method is presented for the design of controllers and observers that results in the deadbeat behaviour of a class of linear multivariable discrete-time plants with inaccessible state vectors.     

On discrete-time H/sub /spl infin// fixed-lag smoothing

The H/sub /spl infin// fixed-lag smoothing problem for discrete-time linear systems is considered. It is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system. However, in order to check the solvability of the smoothing problem and compute the relevant gains, one must solve a Riccati equation involving the augmented system matrices, which is an approach that may be inefficient, especially for long lags. In this paper, efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H/sub /spl infin// filtering Riccati equation. In particular, this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.     

An unbiased p-step predictive FIR filter for a class of noise-free discrete-time models with independently observed states

The paper addresses a new unbiased p-step toward predictive finite impulse response (FIR) filter for a class of discrete-time deterministic state space models, which states are represented on a horizon of N past points with degree polynomials and observed independently. It is implied that measurements are not available at a current time point n. The problem arises in synchronization and tracking when a signal is lost. Generic coefficients are derived via the Bernoulli polynomials for a two-parameter family of the polynomial filter gains. A generalization is provided for the linear (ramp) and quadratic filter gains. We show that the solution proposed is efficient in applications to predictive filtering of the states of local clocks of digital communication network nodes when a synchronizing signal is temporarily not available.