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1

Recurrence classification for a family of non-linear storage models

Glynn P. W., Glynn J. E., Rai S.

Probability and Mathematical Statistics

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2017

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Vol. 37, Fasc. 2

337--353

EN

Necessary and sufficient conditions for positive recurrence of a discrete-time non-linear storage model with power law dynamics are derived. In addition, necessary and sufficient conditions for finiteness of p-th stationary moments are obtained for this class of models.

2

Local dynamics in a Leslie-Gower system model

Dragomirescu F. I., Caruntu B., Georgescu R. M.

Journal of Mathematics and Applications

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2011

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Vol. 34

15-26

EN

Mathematical ecology or/and biology requires the study of populations that interact. This is the reason for the intensive study of the predator-pray models. A Leslie-Gower model of such type is considered here and the stability properties of its equilibrium points are analyticallyand numerically investigated. Dynamics and bifurcations are deduced. Level curves for corresponding Lyapunov functions for various values of the physical parameters in the parameter space are graphically presented emphasizing the stability regions.

3

Stability analysis of sliding-mode feedback control

Clarke F. H., Vinter R. B.

Control and Cybernetics

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2009

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Vol. 38, no 4A

1169-1192

EN

This paper provides new analytic tools leading to the first rigorous stability and robustness analysis of sliding-mode feedback controllers. Unrestrictive conditions are given, under which these controllers are stabilizing in the presence of large disturbances, conditions invoke the existence of two Lyapunov-type functions, the first associated with passage to the sliding set in finite time, and the second with convergence to the desired state. In this approach, account is taken, from the outset, of implementational constraints. We provide a framework for establishing stability and robustness of the closed-loop system, for a variety of implementation schemes. We illustrate our results by means of two examples of the type frequently encountered in the sliding-mode literature.

4

Non-quadratic performance design for Takagi-Sugeno fuzzy systems

Bernal M., Husek P.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 3

383-391

EN

This paper improves controller synthesis of discrete Takagi-Sugeno fuzzy systems based on non-quadratic Lyapunov functions, making it possible to accomplish various kinds of control performance specifications such as decay rate conditions, requirements on control input and output and disturbance rejection. These extensions can be implemented via linear matrix inequalities, which are numerically solvable with commercially available software. The controller design is illustrated with an example.

5

Iterated function systems generated by strict contractions and place-dependent probabilities

Zaharopol R.

Bulletin of the Polish Academy of Sciences. Mathematics

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2000

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Vol. 48, no 4

429-438

EN

Let (w[sub l], w[sub 2],...,w[sub k];p[sub 1],p[sub 2],...p[sub k]) be an iterated function system (IFS for short) with continuous place-dependent probabilities, defined on a metric space (X, d). Assume that every closed ball in X is compact. Our main result is that the IFS has an attractive probability measure whenever the following three conditions are satisfied: (1) w[sub i] : X --> X is a strict contraction for every i = 1,...,k. (2) sum[...]p[sub i](x)p[sub i](y) > 0 for every x, y [belongs to] X. (3) There exists p > 0 in R such that [...] for every x, y [belongs to] X and j = l, 2,...,k. Note that we do not require the p[sub i]'s to be even uniformly continuous. This research was motivated by a question of Barnsley, Demko, Elton, and Geronimo, [1, p. 373], concerning IFS which satisfy only condition (1). We construct a family C of IFS which we use to answer the question. Our main result allows us to distinguish IFS in C which possess attractive probabilities.