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We study stability and stabilizability properties of systems with discontinuous right hand-side (with solutions intended in Filippov’s sense) by means of locally Lipschitz continuous and regular Lyapunov functions. The stability result is obtained in the more general context of differential inclusions. Concerning stabilizability, we focus on systems affine… (More)
We consider continuous-time average consensus dynamics in which the agents’ states are communicated through uniform quantizers. Solutions to the resulting system are defined in the Krasowskii sense and are proven to converge to conditions of “practical consensus”. To cope with undesired chattering phenomena we introduce a hysteretic quantizer, and we study… (More)
This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The key technical difficulty in the study of these dynamics is that the right-hand sides of the equations are discontinuous… (More)
The aim of this paper is to suggest a modification to the usual bounded confidence model of opinion dynamics, so that “changes of opinion” (intended as changes of the sign of the initial state) of an agent are never induced by the dynamics. In order to do so, a bipartite consensus model is used, endowing it with a confidence range. The resulting signed… (More)
This paper deals with a quantized version of a consensus dynamics in continuous-time, which is motivated by opinion dynamics applications. Under the assumption of all-to-all communication, we show existence and completeness of solutions, we characterize the equilibria, and we prove asymptotical convergence to a state of quantized consensus. For almost all… (More)
The problem of deploying continuous-time kinematic agents on a line is considered. To achieve the prescribed formation each agent uses a binary information, namely whether the distance of the agent from a neighbor is below or above the prescribed inter-agent distance. A simple control law which achieves and maintains the formation despite the coarse… (More)
This report studies a continuous-time version of the well-known Hegselmann-Krause model of opinion dynamics with bounded confidence. As the equations of this model have discontinuous right-hand side, we study their Krasovskii solutions. We present results about existence and completeness of solutions, and asymptotical convergence to equilibria featuring a… (More)
In this paper we consider the classical problem of stabilizing nonlinear systems in the case the control laws take values in a discrete set. First, we present a robust control approach to the problem. Then, we focus on the class of dissipative systems and rephrase classical results available for this class taking into account the constraint on the control… (More)
Differential equations with discontinuous righthand side and solutions intended in Carathéodory sense are considered. For these equations sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.
The main result of this note is an external stabilizability theorem for discontinuous systems affine in the control (with solutions intended in the Filippov’s sense). In order to get it we first prove a sufficient condition for external stability which makes use of nonsmooth Lyapunov-like functions.