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Time-Periodic State Estimation with Event-Based Measurement Updates
Published in Marek Miskowicz, Event-Based Control and Signal Processing, 2018
Joris Sijs, Benjamin Noack, Mircea Lazar, Uwe D. Hanebeck
£ G R"15". The Minkowski sum of two sets Cx,C2 G R" is denoted as C ® C2 := {x + ylx G Cx,y G C2}. The null-matrix and identity-matrix of suitable dimensions (clear from the context) are denoted as 0 and I, respectively. For a continuous-time signal x(t), where tk G R+ denotes the time of the k-th sample, let us define x[k] := x(tk) and x(t0:k) := (x(t0), x(ti), • • • ,x(tk)). The q-th element of a vector x G R" is denoted as {x}q, while {A}qr denotes the element of a matrix A G Rmxn in the q-th row and r-th column. The transpose, determinant, inverse, and trace of a matrix A G R"X" are denoted as AT, |A|, A—1, and tr(A), respectively. The minimum and maximum eigenvalue of a square matrix A are denoted as Xmin(A) and Xmax(A), respectively. The p-norm of a vector x G R" is denoted
A survey of fundamental operations on discrete convex functions of various kinds
Published in Optimization Methods and Software, 2021
The Minkowski sum of an M-convex set with an integer box is not necessarily M-convex. See Example 3.21.The Minkowski sum of a constant-parity jump system with an integer box is not necessarily a constant-parity jump system. See Example 3.21.The Minkowski sum of a discrete midpoint convex set with an integer box is not necessarily discrete midpoint convex. See Example 3.22.The Minkowski sum of a multimodular set with an integer box is not necessarily multimodular. See Example 3.18.
Optimality conditions for mixed discrete bilevel optimization problems
Published in Optimization, 2018
S. Dempe, F. Mefo Kue, P. Mehlitz
Let be an arbitrary norm in and be the Euclidean inner product. The symbol denotes the absolute value sum norm. For any set , , , , , , and denote the convex hull of C, the conic hull of C, the closure of C, the boundary of C, the interior of C, and the annihilator of C (i.e. the set ), respectively. Take some point . Then represents the Minkowski sum of the singleton and the set C. If holds, we define the Bouligand tangent cone (or contingent cone) to C at c as stated below:
Analytical method on stabilisation of fractional-order plants with interval uncertainties using fractional-order PIλ Dμ controllers
Published in International Journal of Systems Science, 2019
Supposing that with , the vertex functions of the value set are determined by for and for based on Minkowski sum operation at . The number of the vertices is in the value set .