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Summary: In this paper, a distributed command governor (CG) strategy is introduced that, by the use of graph colorability theory, improves the scalability property and the performance of recently introduced distributed noncooperative sequential CG strategies. The latter are characterized by the fact that only 1 agent at a decision time is allowed to update its command, whereas all the others keep applying their previously computed commands. The scalability of these early CG distributed schemes and their performance are limited because the structure of the constraints is not taken into account in their implementation. Here, by exploiting the idea that agents that are not directly coupled by the constraints can simultaneously update their control actions, the agents in the network are grouped into particular subsets (turns). At each time instant, on the basis of a round‐robin policy, all agents belonging to a turn are allowed to update simultaneously their commands, whereas agents in other turns keep applying their previous commands. Then, a turn‐based distributed CG strategy is proposed and its main properties are analyzed. Graph colorability theory is used to determine the minimal number of turns and to distribute each agent in at least a turn. A novel graph colorability problem that allows one to maximize the frequency at which agents can update their commands is proposed and discussed. A final example is presented to illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, the robust stability problem for uncertain linear continuous-time systems is faced making use of piecewise quadratic Lyapunov functions (PQLF). PQLF are obtained by partitioning the state space into polyhedral cones and by associating a quadratic form with each cone. The proposed formulation allows us to recover, as particular cases of PQLFs, not only the class of quadratic functions but also the class of polyhedral functions. In this way, we manage to show the universality of the class of PQLF for the robust stability problem. The main contribution of the paper is the formulation of a low-computational cost procedure for the stability analysis of uncertain linear systems. Several numerical examples are included in the paper, where the proposed approach is tested on some benchmark cases taken from the literature. Comparisons with existing methods show that the proposed method performs better under several aspects. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]