Synchronization control in arrays of identical output-coupled continuoustime linear systems is studied. Sufficiency of new conditions for the existence of a synchronizing feedback law are analyzed. It is shown that for neutrally stable systems that are detectable form their outputs, a linear feedback law exists under which any number of coupled systems synchronize provided that the (directed, weighted) graph describing the interconnection is fixed and connected. An algorithm generating one such feedback law is presented. It is also shown that for critically unstable systems detectability is not sufficient, whereas full-state coupling is, for the existence of a linear feedback law that is synchronizing for all connected coupling configurations.
A basic result in synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their outputs and neutrally stable, it is shown that a linear output feedback law exists under which the coupled systems globally asymptotically synchronize for all fixed connected (asymmetrical) network topologies. An algorithm is provided to compute such feedback law based on individual system parameters.
We provide a less conservative (compared with our previous results) lower bound on the horizon length for a stabilizing model predictive control algorithm where the terminal cost is not assumed to be a local control Lyapunov function. Our main additional assumption is that the value function is bounded by a linear function of a measure of the state uniformly in the horizon length.
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