Abstract-Nonlinear cooperative systems associated to vector fields that are concave or subhomogeneous describe well interconnected dynamics that are of key interest for communication, biological, economical and neural network applications. For this class of positive systems, we provide conditions that guarantee existence, uniqueness and stability of strictly positive equilibria. These conditions can be formulated directly in terms of the spectral radius of the Jacobian of the system. If control inputs are available, then it is shown how to use state feedback to stabilize an equilibrium point in the interior of the positive orthant.
In this paper we address the problem of information-constrained optimal control for an interconnected system subject to one-step communication delays and power constraints. The goal is to minimize a finite-horizon quadratic cost by optimally choosing the control inputs for the subsystems, accounting for power constraints in the overall system and different information available at the decision makers. To this purpose, due to the quadratic nature of the power constraints, the LQG problem is reformulated as a linear problem in the covariance of state-input aggregated vector. The zeroduality gap allows us to equivalently consider the dual problem, and decompose it into several sub-problems according to the information structure present in the system. Finally, the optimal control inputs are found in a form that allows for offline computation of the control gains.
Abstract-Contractive interference functions are a subclass of the standard interference functions used in the design and analysis of distributed power control algorithms for wireless networks. Their peculiarity is that for the resulting positive system the existence and global asymptotic stability of a unique positive equilibrium point is guaranteed. In this paper we give an infinitesimal characterization of nonlinear contractive interference functions in terms of the spectral radius of the Jacobian linearization at any point in the positive orthant. The condition we obtain, that the spectral radius is always less than 1, extends to the nonlinear case an equivalent property of linear interference functions, and leads to a Jacobian characterization similar to the one commonly used in contraction analysis of nonlinear systems.
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