The problem of minimizing the maximum transient energy growth is considered. This problem has importance in some fluid flow control problems and other classes of nonlinear systems. Conditions for the existence of static controllers that ensure strict dissipativity of the transient energy are established and an explicit parametrization of all such controllers is provided. It also is shown that by means of a -parametrization, the problem of minimizing the maximum transient energy growth can be posed as a convex optimization problem that can be solved by means of a Ritz approximation of the free parameter. By considering the transient energy growth at an appropriate sequence of discrete time points, the minimal maximum transient energy growth problem can be posed as a semidefinite program. The theoretical developments are demonstrated on a numerical example.Abstract-We examine the consensus problem for a group of agents that communicate via a stochastic information network. Communication among agents is modeled as a weighted directed random graph that switches periodically. The existence of any edge is probabilistic and independent from the existence of any other edge. We further allow each edge to be weighted differently. Sufficient conditions for asymptotic almost sure consensus are presented for the case of positive weights and for the case of arbitrary weights.
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