Stabilization Of Polynomial Systems Research Articles

Stabilization of polynomial systems in ℝ3 via homogeneous feedback

Abstract In this paper, we study the stabilization problem of a class of polynomial systems of odd degree in dimension three. The constructed stabilizing feedback is homogeneous and guarantee the homogeneity of the closed loop system.mynotered In the end of the paper, we show the efficiency of such a study in the local stabilization of nonlinear systems affine in control.

Stabilizing kinetic feedback design using semidefinite programming

Abstract: A novel state feedback design method is proposed in this paper for the stabilization of polynomial systems with linear input structure. Using a static nonlinear feedback, the open loop system is transformed to a complex balanced kinetic closed loop system with stoichiometric subspace having maximum dimension, that is known to be stable. The feedback law is computed using semidefinite programming where the objective function is used to adjust the performance of the closed-loop system by tuning the largest eigenvalue of the state matrix of the linearized closed-loop system. The approach is illustrated on a purely computational example followed by a simple process system example.

STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

This paper investigates the stability of (switched) polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a (switched) polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some su±cient conditions for the global stability of polynomial systems.