A remark on abstract multiplier conditions for robustness problems
نویسندگان
چکیده
This paper presents a generalization of recent results of Açıkmeşe and Corless [B. Açıkmeşe, M. Corless, Stability analysiswith quadratic Lyapunov functions: Somenecessary and sufficientmultiplier conditions, Systems Control Letters 57 (2008) 78–94] concerning multiplier conditions of quadratic stability of uncertain/nonlinear systems. Abstract full block S-procedure results are formulated, extending the results of Scherer [C.W. Scherer, LPV control and full block multipliers, Automatica 37 (2001) 361–375] for such cases when the sets representing the uncertainties do not necessarily have subspace structure. The main contribution of the present work is the investigation of the conditions under which the results of Scherer and Açıkmeşe and Corless can be formulated in a unified framework. © 2008 Elsevier B.V. All rights reserved.
منابع مشابه
Analysis of thin plates by a combination of isogeometric analysis and the Lagrange multiplier approach
The isogeometric analysis is increasingly used in various engineering problems. It is based on Non-Uniform Rational B-Splines (NURBS) basis function applied for the solution field approximation and the geometry description. One of the major concerns with this method is finding an efficient approach to impose essential boundary conditions, especially for inhomogeneous boundaries. The main contri...
متن کاملIMPOSITION OF ESSENTIAL BOUNDARY CONDITIONS IN ISOGEOMETRIC ANALYSIS USING THE LAGRANGE MULTIPLIER METHOD
NURBS-based isogeometric analysis (IGA) has currently been applied as a new numerical method in a considerable range of engineering problems. Due to non-interpolatory characteristic of NURBS basis functions, the properties of Kronecker Delta are not satisfied in IGA, and as a consequence, the imposition of essential boundary condition needs special treatment. The main contribution of this study...
متن کاملKarush-Kuhn-Tucker Conditions for Nonsmooth Mathematical Programming Problems in Function Spaces
Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to L-minimum norm control problems, L∞norm minimization, and a class of ...
متن کاملNormal Forms of Necessary Conditions for Dynamic Optimization Problems with Pathwise Inequality Constraints
There has been a longstanding interest in deriving conditions under which dynamic optimization problems are normal, that is, the necessary conditions of optimality (NCO) can be written with a nonzero multiplier associated with the objective function. This paper builds upon previous results on nondegenerate NCO for trajectory constrained optimal control problems to provide even stronger, normal ...
متن کاملExplicit Implicit Function Theorem for All Fields
Remark 1. The conditions P (X, f(X)) = 0 and f(0) = 0 imply that P (0, 0) = 0. As P ′ Y (0, 0) is also 0, the sums in both expressions of [X]f are finite. Remark 2. When P (X,Y ) = Xφ(Y ), where φ(X) ∈ K[[X ]] and φ(0) 6= 0, we obtain the Lagrange inversion formula [X]f = [Y ](φ(X) − Y φ(X)φ(X)). If the characteristic of K is 0, we also have the following form [X]f = [Y ]φ(Y ). Remark 3. When P...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Systems & Control Letters
دوره 58 شماره
صفحات -
تاریخ انتشار 2009