This paper deals with the problems of robust stability analysis and robust stabilization for uncertain nonlinear polynomial systems. The combination of a polynomial system stability criterion with an improved robustness measure of uncertain linear systems has allowed the formulation of a new criterion for robustness bound estimation of the studied uncertain polynomial systems. Indeed, the formulated approach is extended to involve the global stabilization of nonlinear polynomial systems with maximization of the stability robustness bound. The proposed method is helpful to improve the existing techniques used in the analysis and control for uncertain polynomial systems. Simulation examples illustrate the potentials of the proposed approach. 1. Introduction Being subject of considerable theoretical and practical significance, stability analysis and control of nonlinear dynamic systems have been attracting the interest of investigators for several decades [1–3]. The essential aim of robust analysis and nonlinear robust control theory is to internally stabilize the nonlinear plant while maximizing the upper bound on the parametric perturbations, such that the perturbed nonlinear system remains stable, as described in [4–8]. However, each of the published approaches on this subject concerns particular classes of nonlinear uncertain systems and there is no standard method to investigate robust stability and stabilization of general high-order nonlinear systems [9–13]. Therefore, in deep contrast with linear analysis and control methods, which are flexible, efficient and allowing to solve a broad class of linear control problems, there are few practical methods in nonlinear control which can handle real engineering problems with similar comfort. In this paper, we are concerned with further developments of robust stability and feedback stabilization methods of a class of nonlinear polynomial systems with structured uncertainties. Our motivations for studying polynomial systems mainly comes from the fact that they provide a convenient unified framework for mathematical modelling of many physical processes and practical applications such as electrical machines and robot manipulators, and also the ability to approach any analytical nonlinear dynamical systems, since, any nonlinear system can be developed into a polynomial form by Taylor series expansions [14–17]. Moreover, the description of polynomial systems can be simplified using the Kronecker product and power of vectors and matrices [18]. The parameter uncertainties in the studied polynomial systems are
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