Application of stochastic artsteins theorem to feedback stablization

The stochastic Artstein's theorem is applied to derive sufficient conditions for dynamic asymptotic stabilization in probability by means of a feedback integrator for a class of nonlinear stochastic differential systems. A stabilizing feedback law is deduced from a control Lyapunov function     

Stabilization of a class of nonlinear composite stochastic systems

This paper deals with the stability for a class of nonlinear composite stochastic systems by feedback laws.Firstly,we give sufficient conditions for the existence of feedback laws which render the equilibrium solution of the stochastic system globally asymptotically stable in probability.Secondly,for stochastic systems of the same type,we prove that there exists a linear feedback law which exponentially stabilizes in mean square the closed–loop stochastic system at its equilibrium.     

Robust Stability and Stabilization of a Class of Nonlinear Itô-Type Stochastic Systems via Linear Matrix Inequalities

This article presents a new approach to robust quadratic stabilization of nonlinear stochastic systems. The linear rate vector of a stochastic system is perturbed by a nonlinear function, and this nonlinear function satisfies a quadratic constraint. Our objective is to show how linear constant feedback laws can be formulated to stabilize this type of stochastic systems and, at the same time maximize the bounds on this nonlinear perturbing function which the system can tolerate without becoming unstable. The new formulation provides a suitable setting for robust stabilization of nonlinear stochastic systems where the underlying deterministic systems satisfy the generalized matching conditions. Our sufficient conditions are written in matrix forms, which are determined by solving linear matrix inequalities (LMIs), which have significant computational advantage over any other existing techniques. Examples are given to demonstrate the results.     

Finite-dimensional controller design for semilinear parabolic systems

This paper considers the stabilization of steady-state solutions of a semilinear parabolic system using finite-dimensional feedback controllers with support in an arbitrary open subset and which are active in one equation only. It is shown that such a controller, with dimension given by the largest algebraic multiplicity of the unstable eigenvalues of the linearized system, exponentially stabilizes the steady-state solution. An optimal design methodology for these types of controllers, which is based on the finite element approximation of the semilinear parabolic system, is introduced and illustrated by numerical simulation examples.     

Multiple positive periodic solutions of nonlinear functional differential system with feedback control

In this paper, we employ Avery-Henderson fixed point theorem to study the existence of positive periodic solutions to the following nonlinear nonautonomous functional differential system with feedback control:

     

Periodicity and Stability in Periodic <Emphasis Type="Italic">n</Emphasis>-Species Lotka-Volterra Competition System with Feedback Controls and Deviating Arguments

By using the method of coincidence degree and Lyapunov functional, a set of easily applicable criteria are established for the global existence and global asymptotic stability of strictly positive(componentwise)periodic solution of a periodic n-species Lotka-Volterra competition system with feedback controls and several deviating arguments.The problem considered in this paper is in many aspects more general and incorporate as special cases various problems which have been studied extensively in the literature.Moreover,our new criteria,which improve and generalize some well known results, can be easily checked.     

Realistic feedback control of turbogenerators

In this paper, the optimal control of a turboalternator connected to an infinite bus is considered. The alternator is controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a two-point nonlinear boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, contrary to the usual feedback control of a linear model. In contrast to the model used in Ref. 1, the model used here include the transfer functions of the governor, the turbine, and the voltage regulator.This work was supported in part by the National Research Council of Canada, Grant No. A-4146.     

A test for the presence of pure feedback in multivariate dynamic stochastic systems

This paper describes a procedure for testing the presence of a pure feedback loop in a transfer function model for a multivariate discrete dynamic stochastic system. A modification of the portmanteau statistic based on sample cross-covariance matrices of the prewhitened series is proposed. The statistic is shown to be asymptotically distributed according to a % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gaeq4Xdm2aaWbaaSqabeaacaaIYaaaaaaa!3E0C!\[\chi ^2 \]-distribution with certain degrees of freedom under some pure feedback assumptions. Some numerical results are given to show the behavior of the proposed method.     

Feedback stabilization of drift cyclotron loss cone instability by modulated electron sources

It is shown that the drift cyclotron loss cone instability can be suppressed by modulating electron density within the plasma. With the feedback in +90° phase the critical density gradient needed for the onset of the drift cyclotron loss cone instability increases approximately linearly with the gain. Typically with the gain of −50Ω _i the critical density gradient can be pushed up by as much as two orders of magnitude and minimum mirror plasma radius can be brought down in the same proportion.