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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)
Aknowledgements I am very pleased to have the opportunity here to express my sincere thanks to Professor Bacciotti who has guided me in the study of mathematics for five years, giving me confidence and transmitting his fondness for this discipline. Particular thanks also to Professor Conti. It has been really a pleasure to attend his course in Control… (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.
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.
In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that… (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)