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This paper provides a new robust control synthesis method for linear uncertain multivariable discretetime systems subject to the ellipsoidal parametric uncertainty. This type of parametric uncertainty is delivered by classical prediction error identification methods in a full-order model structure. The uncertainty is represented by linear fractional transformation. Fixed-order H2 and H∞ control design problems are formulated in terms of solutions to a set of dilated linear matrix inequalities. The control designs build on quadratically parameter-dependent Lyapunov functions. Flexible structures for the auxiliary variables are introduced to improve the performance and reduce the conservatism related to the fixed-order controller synthesis. The employed structures may be updated by a proposed iterative procedure. Numerical examples show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A large group of control problems can be casted as a problem of design for positivity. A new method is presented for choosing a parameter which ensures the robust positiveness of any real analytic function. The method provides an analytic solution as opposed to numerical sampling techniques. The method is especially useful in design for polynomial positivity due to existence of efficient techniques for solution of systems of polynomial equations and inequalities. Examples are provided, which illustrate the applicability of the proposed method to real-life problems. [ABSTRACT FROM PUBLISHER]

In this paper, the robust D‐stability problem (i.e. the robust eigenvalue‐clustering in a specified circular region problem) of linear discrete singular time‐delay systems with structured (elemental) and unstructured (norm‐bounded) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time‐delay system is regular and impulse‐free, and has all its finite eigenvalues lying inside a specified circular region, a new sufficient condition is proposed to preserve the assumed properties when structured and unstructured parameter uncertainties are added into the linear nominal discrete singular time‐delay system. When all the finite eigenvalues are just required to locate inside the unit circle of the z‐plane, the proposed criterion will become the stability robustness criterion. For the case that the linear discrete singular time‐delay system is only subject to structured parameter uncertainties, by an illustrative example, the presented sufficient condition is shown to be less conservative than the existing one reported recently in the literature. [ABSTRACT FROM PUBLISHER]