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Systems with associative dynamics

Ronald Korin Pearson, Ülle Kotta, Sven Nōmm (2002)

Kybernetika

This paper introduces a class of nonlinear discrete-time dynamic models that generalize familiar linear model structures; our motivation is to explore the extent to which known results for the linear case do or do not extend to this nonlinear class. The results presented here are based on a complete characterization of the solution of the associative functional equation F [ F ( x , y ) , z ] = F [ x , F ( y , z ) ] due to J. Aczel, leading to a class of invertible binary operators that includes addition, multiplication, and infinitely many...

Test signal design for failure detection: A linear programming approach

Héctor Scola, Ramine Nikoukhah, François Delebecque (2003)

International Journal of Applied Mathematics and Computer Science

A new methodology for the design of filters that permits failure detection and isolation of dynamic systems is presented. Assuming that the normal and the faulty behavior of a process can be modeled by two linear systems subject to inequality bounded perturbations, a method for the on-line implementation of a test signal, guaranteeing failure detection, is proposed. To improve the fault detectability of the dynamic process, appropriate test signals are injected into the system. All the computations...

The choice of the forms of Lyapunov functions for a positive 2D Roesser model

Tadeusz Kaczorek (2007)

International Journal of Applied Mathematics and Computer Science

The appropriate choice of the forms of Lyapunov functions for a positive 2D Roesser model is addressed. It is shown that for the positive 2D Roesser model: (i) a linear form of the state vector can be chosen as a Lyapunov function, (ii) there exists a strictly positive diagonal matrix P such that the matrix A^{T}PA-P is negative definite. The theoretical deliberations will be illustrated by numerical examples.

Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces

Viorica Mariela Ungureanu (2004)

Bollettino dell'Unione Matematica Italiana

In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.

Variance-Constrained H ∞ finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols

Ming Lyu, Jie Zhang, YuMing Bo (2020)

Kybernetika

In this paper, the variance-constrained H ∞ finite-horizon filtering problem is investigated for a class of time-varying nonlinear system under muti-rate communication network and stochastic protocol (SP). The stochastic protocol is employed to determine which sensor obtains access to the muti-rate communication network in order to relieve communication burden. A novel mapping technology is applied to characterize the randomly switching behavior of the data transmission resulting from the utilization...

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