Quality‐by‐design by skewed spherical structured singular value

Abstract

This study develops numerical algorithms to compute an ellipsoidal set of input parameters, called a design space, that ensures that the system outputs lie within a set of design specifications in quality-by-design. The algorithm is based on a proposed skewed spherical structured singular value ν s , for which this study derives upper bounds and proves the (scaled) main loop theorems and small-gain theorem for the Frobenius norm. Three examples are included to illustrate applications of the numerical algorithms. 2 Mathematical preliminaries The set of real numbers, real vectors of length n, and real matrices of size n × m are denoted by R, R n , and R n×m , respectively. The set of complex numbers, real vectors of length n, and real matrices of size n × m are denoted by C, C n , and C n×m , respectively. For a vector v ∈ R n , v T denotes the transpose of the vector v, v i denotes the ith element of v, and v 2 = √ v T v. For a matrix M ∈ R n×m , M T denotes the transpose of the matrix M , for a matrix

Value-Set-Based Approach to Robust Stability Analysis for Ellipsoidal Families of Fractional-Order Polynomials with Complicated Uncertainty Structure

“…The information about the uncertainty structure must be added. Note that the spherical/ellipsoidal parametric uncertainty itself is, by its definition, always dependent, but the (in)dependency of the uncertainty structure is discussed here.Despite the fact that the spherical/ellipsoidal parametric uncertainty has not been researched so often as the classical box-shaped parametric uncertainty, there is still a range of works dealing with the spherical/ellipsoidal parametric uncertainty and related problems, but, to the best of the authors' knowledge, only for integer-order (IO) systems and not for fractional-order (FO) systems yet, apart from the works addressing the more general infinite-dimensional systems, e.g., [18,19]. Robust pole-placement technique for plants with ellipsoidally uncertain parameters, based on a convex minimax programming, was proposed in [20].…”