Stability Of Two-dimensional Digital Filters Research Articles

Expected power bound and stability of two-dimensional digital filters with multiplicative noise in the FMLSS model

This paper studies the two-dimensional (2-D) expected power bound (EPB) for 2-D digital filters with multiplicative noise in the Fornasini-Marchesini local state-space (FMLSS) model. By virtue of a class of linear matrix inequalities (LMIs), the novel existence criterion of 2-D EPB for 2-D digital filters in the considered model is obtained. The corresponding stabilization controller design method is presented based on the above criterion. Finally, two examples are presented to verify the effectiveness of our results.

Stability of two-dimensional digital filters described by the Fornasini–Marchesini second model with quantisation and overflow

This study discusses new criterion for the global asymptotic stability of two-dimensional digital filters described by the Fornasini–Marchesini second local state-space model under various combinations of quantisation and overflow non-linearities. The criterion is compared with a previously reported criterion.

Lyapunov stability of two-dimensional digital filters with overflow nonlinearities

In this paper, the second method of Lyapunov is utilized to establish sufficient conditions for the global asymptotic stability of the trivial solution of zero-input two-dimensional (2-D) Fornasini-Marchesini state-space digital filters which are endowed with a general class of overflow nonlinearities. Results for the global asymptotic stability of the null solution of the 2-D Fornasini-Marchesini second model with overflow nonlinearities are established. Several classes of Lyapunov functions are used in establishing the present results, including vector norms and the quadratic form. When the quadratic form Lyapunov functions are considered, the present results involve necessary and sufficient conditions under which positive definite matrices can be used to generate Lyapunov functions for 2-D digital filters with overflow nonlinearities.

Asymptotic stability of two-dimensional digital filters under quantization

The stability of 2-D digital filters implemented with two's complement quantization is investigated. The difference equation model is considered for the following cases: (i) quantization after each product and (ii) quantization after a complete sum of products. For both cases, sufficient conditions are established for asymptotic stability. The 2-D state-space Roesser's (1975) model is also considered under two's complement quantization, and a sufficient condition is derived for its stability. Some examples are given to illustrate the results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust stability of two-dimensional digital filters under coefficient perturbation

A bound on allowable weighted additive perturbation in the coefficients of a 2-D stable digital filter from their respective nominal values is determined so that the strict stability of the perturbed-coefficient filter is maintained. The results are suitable for generalization to multidimensional digital filters with real and complex coefficients. Applications of the results may be found in robust stability analysis of digital signal processing and control theory. >

On Kharitonov-type results for complex-coefficient interval Schur polynomials

A Kharitonov-type result for the stability analysis of real Schur polynomials that have been transformed by a new transformation technique has been proposed, and the necessary and sufficient conditions for the stability of the transformed polynomials were developed by P.P. Vaidyanathan (see IEEE Trans. Acoust. Speech Signal Process, vol.38, no.2, p.277-85, 1990). These results are generalized to the case of the complex coefficient, and the stability of the whole transformed family of interval polynomials is proved. The sufficiency conditions of this test for the stability of the original interval polynomial family is commented on, and checking the stability of the required polynomials for low-order cases is addressed. Some illustrative examples are given. The results may be found useful to testing the interval stability of two-dimensional digital filters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Unit Circle Cauchy Index: Definition, Characterization and Polynomial Zero Distribution

The Cauchy index of a rational transfer function evaluated over an interval of the real line has proved a useful tool in various linear systems applications.In this paper, we define the unit circle Cauchy index and give some computational methods of it. This provides a systematic view of many problems and results on unit circle positivity, polynomial root distribution, and stability. Results on positivity of polynomials in z and $z^{ - 1} $ which are real on $| z | = 1$ are relevant in checking discrete positive realness and the stability of two-dimensional digital filters, while results on the zero distribution of a polynomial relative to the boundary of the unit circle are of relevance in studying the stability of discrete-time systems.

A Nyquist-like test for the stability of two-dimensional digital filters

This paper constructs a Nyquist-like test for the stability of two-dimensional digital filters. The test takes the form of a continuum of classical one-variable Nyquist plots parameterized by the elements of the unit circle of the complex plane. Since the parameter space is compact, the test can be accurately approximated by a finite number of classical one-variable Nyquist plots and is therefore readily implemented on a computer.

On the stability of two-dimensional digital filters

This correspondence proposes a method to check the stability of two-dimensional recursive filters. In this method the Jury table is modified and used to check the first condition of Huang's theorem. Some examples are solved to illustrate the method.