Robust D-stability analysis of an induction motor

Abstract

This paper deals with the synthesis of a state feedback control law to reach some desired dynamic performances of an induction motor. The specification on the closed-loop poles is given in terms of clustering region such as the Ellipsoid Matrix Inequality εMI-region or the Extended Ellipsoid Matrix Inequality εεMI-region. The problem of robust matrix root-clustering analysis is studied. The considered matrix is complex and subject to parameter dependent norm-bounded uncertainties. The clustering regions are unions of convex and possibly disjoint and non-symmetric sub-regions of the complex plane. An aggregation technique approach is used to compute a static state feedback control law which performs a partial pole placement. The proposed clustering conditions are then formulated through an LMI approach. The simulation results provide a good compromise between dynamic performances and some robustness aspects of the controlled system.

Unifying Matrix Stability Concepts with a View to Applications

“…Let us introduce the following notations for the matrix classes. [7], [22] - [25]). We define the concept of (∂(D), G, •)-regularity basing on ∂(D)-regularity: a matrix A ∈ M n×n is called (∂(D), G, •)-regular if σ(G • A) ∂(D) = ∅ for any matrix G from the given matrix class G.…”

“…Given a stability region D ⊂ C and a matrix A ∈ M n×n , when a perturbed matrix A = A + ∆ is D-stable? A number of papers are devoted to studying this property, called robust stability, with respect to different stability regions D (see, for example, [7] for EMI regions). Sometimes, special types of perturbations are considered or some information of ∆ is provided, and we have the following description of the uncertain matrix A:…”

“…Theorem 4 (Kharitonov) An interval polynomial (i.e. all the members of the family (7)) is stable if and only if the four Kharitonov polynomials k 1 (z), k 2 (z), k 3 (z), k 4 (z) are stable.…”

“…for the related studies, see [7], [22] - [25]). We define the concept of (∂(D), G, •)-regularity basing on ∂(D)-regularity:…”

“…Let D ⊂ C be an open stability region, denote its boundary by ∂(D). The following concept was introduced in [25]: amatrix A ∈ M n×n is called ∂(D)singular if σ(A) ∂(D) = ∅ and ∂(D)-regular if σ(A) ∂(D) = ∅ (for the related studies, see[7],[22] -[25]). We define the concept of (∂(D), G, •)-regularity basing on ∂(D)-regularity:a matrix A ∈ M n×n is called (∂(D), G, •)-regular if σ(G • A) ∂(D) = ∅ forany matrix G from the given matrix class G.For any subset D 1 ⊆ D we have…”