We study stability and stabilizability properties of systems with dis-continuous 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… (More)
A new convergence criterion for nonlinear systems was recently derived by the first author. The criterion is similar to Lyapunov's second theorem but differs in several respects. In particular, it has a remarkable convexity property in the context of control synthesis. While the set of control Lyapunov functions for a given system may not even be connected,… (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.
By means of Ryan's necessary condition and of some examples, we see how the interpretation of solutions of systems with discontinuous righthand side influences stabilizability results for systems which do not admit continuous stabilizing feedback laws.
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)
Differential equations with discontinuous righthand side and solutions intended in Carathéodory sense are considered. For these systems sufficient conditions which guarantee both Lyapunov stability and asymptotic stability in terms of nonsmooth Lyapunov functions are given. An invariance principle is also proven.
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 dis-continuous… (More)