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We study the stability properties of linear time-varying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and rendezvous tasks and synchronization problems. The equilibrium set contains all states with identical state components. We present sufficient conditions guaranteeing uniform exponential stability of this equilibrium set, implying that all state components converge to a common value as time grows unbounded. Furthermore it is shown that this convergence result is robust with respect to an arbitrary delay, provided that the delay affects only the off-diagonal terms in the differential equation.

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This paper develops a unified framework for studying robustness of the input-to-state stability (ISS) property and presents new results on robustness of ISS to slowly varying parameters, to rapidly varying signals, and to generalized singular perturbations. The common feature in these problems is a timescale separation between slow and fast variables which permits the definition of a boundary layer system like in classical singular perturbation theory. To address various robustness problems simultaneously, the asymptotic behavior of the boundary layer is allowed to be complex and it generates an average for the derivative of the slow state variables. The main results establish that if the boundary layer and averaged systems are ISS then the ISS bounds also hold for the actual system with an offset that converges to zero with the parameter that characterizes the separation of timescales. This result is then applied to classical robustness problems and various extensions are achieved.

Abstruct-We study a simple but compelling model of n interacting agents with time-dependent, bidirectional and unidirectional communication. The model finds wide application in a variety of fields including swarming, synchronization and distributed decision making. In the model, each agent updates his current state based upon the current information meived from other agents according to a simple weighted average rule. Necessary and/or s a c i e n t conditions for the convergence of the individual agents' states to a common value are presented, extending recent results reported in the Literature. Further, it is observed that more communication dws not necessarily lead to better convergence and may eventually even lead to a loss of convergence, even for the simple models discnssed in the present paper.