We consider a linear plant with decentralized input saturation, whose limits are not necessarily symmetric. We propose a nonlinear static state feedback stabilizer that is asymmetric, in such a way that the non-symmetric nature of the saturation is fully exploited in the control design, for larger regions of attraction. We show by example that the proposed technique provides significantly larger regions of attractions as compared to the symmetric solution results, in a case where the positive and negative saturation limits are different.

Given a social network where the individuals know the identity of the other members, we present a model of opinion dynamics where the connectivity among the individuals depends on both their current and past opinions. Thus, their interactions are not only based on the present states but also on their past relationships. The model is a multi-agent system with active or inactive pairwise interactions depending on auxiliary state variables filtering the instantaneous opinions, thereby taking the past experience into account. When an interaction is (de)activated, a jump occurs, leading to a hybrid model. The proven stability properties ensure that opinions converge to local agreements/clusters as time grows. Simulation results are provided to illustrate the theoretical guarantees.