1,721,240 research outputs found
Pepe (P.) - Présentation des statistiques.
No full textMilhau Jules. Pepe (P.) - Présentation des statistiques.. In: Revue économique, volume 13, n°1, 1962. p. 151
Pepe (P.) - Présentation des statistiques.
No full textMilhau Jules. Pepe (P.) - Présentation des statistiques.. In: Revue économique, volume 13, n°1, 1962. p. 151
A NONLINEAR VERSION OF HALANAY'S INEQUALITY FOR THE UNIFORM CONVERGENCE TO THE ORIGIN
No full textA nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown
On Lyapunov Methods for Nonlinear Discrete-Time Switching Systems with Dwell-Time Ranges
No full textA novel Lyapunov methodology for the stability check of nonlinear discrete-time switching systems, equipped with switches digraphs and non-uniform dwell-time ranges, is here presented. The novelty of the methodology consists in the following coexisting features: i) the global uniform (with respect to compact sets of initial conditions and swtiching signals) asymptotic stability is addressed; ii) the information on allowed switches and (non-uniform) dwell-time ranges is fully exploited; iii) no assumption is introduced on either stability or instability of the subsystems; iv) no assumption is introduced on the regularity of the functions describing the dynamics; v) the number of involved Lyapunov functions is always equal to the number of different modes; vi) a set of Lyapunov inequalities is uniquely defined coping with all scenarios of allowed switches and dwell-time ranges; vii) the provided Lyapunov conditions are necessary and sufficient for the global uniform asymptotic stability
Converse Lyapunov Theorems for Discrete-Time Switching Systems with Given Switches Digraphs
No full textIt is proved in this paper that the existence of suitable multiple Lyapunov functions is a necessary and sufficient condition for a discrete-time nonlinear switching system, with given switches digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the switches digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions
On global exponential stability of discrete-time switching systems with dwell-time ranges: Novel induced LMIs for linear systems with delays
No full textIn this paper, we provide necessary and sufficient Lyapunov conditions for discrete -time switching systems to be globally exponentially stable, when the switching signal obeys to a switches digraph and is subject to dwell -time constraints. In order to best exploit the information on switching -dwelling constraints, conditions are given by means of multiple Lyapunov functions. The number of involved Lyapunov functions is equal to the number of switching modes. To avoid a pileup of Lyapunov functions, we do not introduce dummy vertices that account for dwell -time ranges. For example, in the linear case, such a pileup corresponds to a pileup of decision matrices related to some linear matrix inequalities. A link between global exponential stability and exponential input -to -state stability is provided. The following result is proved: if, in the case of zero input, the discrete -time switching system is globally exponentially stable, and the functions describing the dynamics of the subsystems, with input, are suitably globally Lipschitz, then the switching system is exponentially input -to -state stable. Finally, exploiting the well known relationship between discrete -time systems with delays and discrete -time switching systems, the provided results are shown for the former systems, in the linear case. In particular, linear matrix inequalities, by which the global exponential stability of linear discrete -time systems with constrained time delays can be possibly established, are provided. The utility of these linear matrix inequalities is shown with a numerical example taken from the literature
ISS small-gain theorem for networked discrete-time switching systems
No full textIn this paper it is proved that a networked discrete-time switching system, equipped with a given switches digraph, is input-to-state stable, provided that there exist multiple Lyapunov functions (one for each mode) for each subsystem in the network, satisfying suitable standard inequalities, and provided that a set of suitable vector small-gain conditions are satisfied. The small-gain theorem here provided for the input-to-state stability takes into account the switches digraph. That is, the less is the number of edges in the switches digraph, the less is the number of involved Lyapunov inequalities and small-gain conditions which, if satisfied, guarantee the input-to-state stability of the entire switching system under study. The multiple Lyapunov functions for the entire system, guaranteeing the input-to-state stability, are determined by the multiple Lyapunov functions for each subsystem in the family. To the author's best knowledge, this is the first paper in the literature concerning small-gain theorems for the input-to-state stability of nonlinear discrete-time switching systems with given switches digraphs
Pepe P. et Tisserand-Périer M. Méthodes statistiques dans les sciences humaines
No full textM. T. L. Pepe P. et Tisserand-Périer M. Méthodes statistiques dans les sciences humaines. In: Population, 19ᵉ année, n°3, 1964. pp. 609-610
Pepe P., Tisserand-Perrier P., Méthodes statistiques dans les sciences humaines.
No full textJamous Henri. Pepe P., Tisserand-Perrier P., Méthodes statistiques dans les sciences humaines.. In: Revue française de sociologie, 1964, 5-1. p. 85
Lyapunov-Krasovskii Characterizations of Stability Notions for Switching Retarded Systems
No full textIn this article, we characterize the global asymptotic and exponential stability of nonlinear switching retarded systems through direct and converse Lyapunov-Krasovskii theorems. Thanks to these theorems, a link between the exponential stability of an unforced switching retarded system and the input-to-state stability property is obtained. An example illustrating the applicability of our results is given
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