Displaying similar documents to “The choice of the forms of Lyapunov functions for a positive 2D Roesser model”

Independence of asymptotic stability of positive 2D linear systems with delays of their delays

Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

It is shown that the asymptotic stability of positive 2D linear systems with delays is independent of the number and values of the delays and it depends only on the sum of the system matrices, and that the checking of the asymptotic stability of positive 2D linear systems with delays can be reduced to testing that of the corresponding positive 1D systems without delays. The effectiveness of the proposed approaches is demonstrated on numerical examples.

Positive 2D discrete-time linear Lyapunov systems

Przemysław Przyborowski, Tadeusz Kaczorek (2009)

International Journal of Applied Mathematics and Computer Science

Similarity:

Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching

Guisheng Zhai, Xuping Xu (2010)

International Journal of Applied Mathematics and Computer Science

Similarity:

We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions...

Computer methods for stability analysis of the Roesser type model of 2D continuous-discrete linear systems

Mikołaj Busłowicz, Andrzej Ruszewski (2012)

International Journal of Applied Mathematics and Computer Science

Similarity:

Asymptotic stability of models of 2D continuous-discrete linear systems is considered. Computer methods for investigation of the asymptotic stability of the Roesser type model are given. The methods require computation of eigenvalue-loci of complex matrices or evaluation of complex functions. The effectiveness of the stability tests is demonstrated on numerical examples.

Iterative estimators of parameters in linear models with partially variant coefficients

Shaolin Hu, Karl Meinke, Rushan Chen, Ouyang Huajiang (2007)

International Journal of Applied Mathematics and Computer Science

Similarity:

A new kind of linear model with partially variant coefficients is proposed and a series of iterative algorithms are introduced and verified. The new generalized linear model includes the ordinary linear regression model as a special case. The iterative algorithms efficiently overcome some difficulties in computation with multidimensional inputs and incessantly appending parameters. An important application is described at the end of this article, which shows that this new model is reasonable...

Elimination of finite eigenvalues of the 2D Roesser model by state feedbacks

Tadeusz Kaczorek (2001)

International Journal of Applied Mathematics and Computer Science

Similarity:

A new problem of decreasing the degree of the closed-loop characteristic polynomial of the 2D Roesser model by a suitable choice of state feedbacks is formulated. Sufficient conditions are established under which it is possible to choose state feedbacks such that the non-zero closed-loop characteristic polynomial has degree zero. A procedure for computation of the feedback gain matrices is presented and illustrated by a numerical example.

On an invariant design of feedbacks for bilinear control systems of second order

Vasiliy Belozyorov (2001)

International Journal of Applied Mathematics and Computer Science

Similarity:

The problem of linear feedback design for bilinear control systems guaranteeing their conditional closed-loop stability is considered. It is shown that this problem can be reduced to investigating the conditional stability of solutions of quadratic systems of differential equations depending on parameters of the control law. Sufficient conditions for stability in the cone of a homogeneous quadratic system are obtained. For second-order systems, invariant conditions of conditional asymptotic...