We address the problem of exponential stabilization in probability of the linearized Navier–Stokes equations in an equilibrium point. This is done by designing a linear stochastic feedback controller with support in a point or on a discrete set of points of the domain. This controller consists of steady-state impulse component with support in a finite set of points modulated by an unsteady feed...

We consider the problem of robust state-feedback stabilization for a multi-channel system in a game-theoretic framework. Specifically, we provide a sufficient condition for the existence of a robust feedback Nash equilibrium when every agent aims to optimize a different type of objective function while each function being associated with certain dissipativity properties of the system. We furthe...

Two complementary analyses of a cyclic negative feedback system with delay are considered in this paper. The first analysis applies the work by Sontag, Angeli, Enciso and others regarding monotone control systems under negative feedback, and it implies the global attractiveness towards an equilibrium for arbitrary delays. The second one concerns the existence of a Hopf bifurcation with respect ...

Recent work has shown the benefit of using proportional feedback in TCP/AQM networks. By proportional feedback we mean the marking probability is proportional to the instantaneous queue length. Our earlier work relied on linearization of nonlinear fluidflow models of TCP. In this work we address these nonlinearities directly and establish some stability results when the marking is proportional....

Discrete-time nonlinear feedback control laws are derived for multivariable nonlinear processes, whose “delay-free” parts are minimum phase. These include mixed errorand state-feedback, error-feedback, and mixed errorand output-feedback laws, which can induce linear input output closed-loop response. This study is carried out within the framework of the discrete-time globally linearizing contro...

We prove that TCP Vegas globally converges to its equilibrium point in finite time assuming no feedback information delay. We analyze a continuous-time TCP Vegas model with discontinuity and high nonlinearity. Using the upper right-hand derivative and applying the comparison lemma, we cope with the discontinuous signum function in the TCP Vegas model; using a change of state variables, we deal ...

We study nonlinear control systems in the plane, affine with respect to control. We introduce two sets of feedback equivariants forming a phase portrait PP and a parameterized phase portrait PPP of the system. The phase portrait PP consists of an equilibrium set E, a critical set C (parameterized, for PPP), an optimality index, a canonical foliation and a drift direction. We show that under wea...

The main result of the paper states that almost any analytic single-input control system, which is truly nonlinear, that is not feedback linearizable, with controllable linearization at an equilibrium point, does not admit any symmetry preserving that point. By almost any system, we mean that we exclude a small class of odd systems, that admit just one nontrivial symmetry conjugated to minus id...

We study a feedback stabilization problem for a first-order hyperbolic partial differential equation. The problem is inspired by the stabilization of equilibrium age profiles for an age-structured chemostat, using the dilution rate as the control. Two distinguishing features of the problem are that (a) the PDE has a multiplicative (instead of an additive) input and (b) the state is fed back to ...

In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the brink of extinction become globally stable, but under the conditions of small feedback control on predator, ...