On Input-to-Output Stability and Robust Synchronization of Generalized Persidskii Systems

Abstract

In this paper, we study a class of generalized Persidskii systems with external disturbances and establish conditions, in the form of linear matrix inequalities, for input-to-output stability (IOS) and robust synchronization for these systems. We apply the obtained results to the robust control design for synchronizing linear systems and to the synchronization of Hindmarsh-Rose models of neurons.

Annular short-time stability of generalized Persidskii systems

“…Following [28], [16], [22], [23], the stability analysis of (2) can be performed using a Lyapunov function…”

“…The considered class of nonlinear dynamics in this paper is called the generalized Persidskii systems, which have been extensively studied in the context of neural networks [15], biological models [16], and power systems [17], and whose original form was introduced in [18], [19], [20]. Recently the conditions of input-to-state stability, input-tooutput stability, and convergence, as well as the synthesis of a state observer have been established in [21], [16], [22], [23] for generalized Persidskii models.…”

“…The considered class of nonlinear dynamics in this paper is called the generalized Persidskii systems, which have been extensively studied in the context of neural networks [15], biological models [16], and power systems [17], and whose original form was introduced in [18], [19], [20]. Recently the conditions of input-to-state stability, input-tooutput stability, and convergence, as well as the synthesis of a state observer have been established in [21], [16], [22], [23] for generalized Persidskii models. Note that most existing approaches to synthesizing Lyapunov functions for stability analysis in nonlinear dynamics involve various canonical forms of the studied differential equations, such as Lur'e systems [24], homogeneous models [25], Persidskii systems [18], and Lipschitz dynamics, and the presence of nonlinearities leads to that the established stability conditions can be rather complicated.…”

On Delay-Dependent Conditions of ISS for Generalized Persidskii Systems

“…Such a choice is motivated by the existence of several canonical forms of Lyapunov functions for a Persidskii system [9], [12], [13]. In addition, due to recent advancements in [14], [15], the ISS and input-tooutput stability (IOS) conditions are constructively formulated using linear matrix inequalities (LMIs). Our main goal is to extend these results to the delay-dependent conditions of input-to-state stability and stabilization for generalized Persidskii systems with time delays a based on the Lyapunov-Krasovskii functional approach, whose form is proposed specifically for the considered class of models.…”

A class of nonlinear state observers for an SIS system counting primo-infections

“…Section II recalls the model under study (system (1) below), transformed by a change of coordinates into a Persidskii system form [16], [10], [9], for which a class of observers is proposed. The asymptotic convergence of the latter is established in Section III under adequate assumptions on the gain coefficients and using techniques inspired from [13], [14]. Numerical simulations are provided in Section IV before some concluding remarks in Section V. For the sake of space, all proofs are omitted and will be published in an upcoming research report.…”