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This article presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Itô stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonconvex, its equivalent convex formulation is proposed utilizing SDC parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with ${\bf \mathcal {L}_2}$ -robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, $\mathcal {H}_\infty$ , and baseline nonlinear controllers for spacecraft attitude control and synchronization problems. [ABSTRACT FROM AUTHOR]

We derive an explicit characterization of the stability region of stationary multi-queue multi-server (MQMS) queueing system by means of a finite set of linear inequalities. More specifically, we explicitly determine the coefficients of the linear inequalities describing the facet-defining hyperplanes of the stability region polytope. Such a characterization is useful for performance evaluation of certain scheduling algorithms such as maximum weight (MW) policy. Our results can be used for studying the asymptotic behavior of the MW policy and computing bounds for the average queueing delay, as well as limiting moments of the queue sizes in heavy-traffic regime. Furthermore, it may be directly applied as the constraint set of network stochastic optimization problems to provide an offline computational solution for such problems. Finally, we use our methodology to characterize the stability region of a fluid model MQMS system which is described by an infinite number of linear inequalities. For such a model, we present an example and show that depending on the channel distribution, the stability region can be instead characterized by a finite set of non-linear inequalities. [ABSTRACT FROM AUTHOR]