Max-algebra, where the classical arithmetic operations of addition and multiplication are replaced by a ⊕ b := max(a, b) and a ⊗ b := a + b offers an attractive way for modelling discrete event systems and optimization problems in production and transportation. Moreover, it shows a strong similarity to classical linear algebra: for instance, it allows a consideration of linear equation systems ...

This article developed a new result on the eigenvalue distribution for a certain class of time delay systems based on the extension of the Hermite-Biehler Theorem. Such result is applied to proportional-integral (PI) controller parameter design for a first-order plant with time delay via eigenvalue assignment. Using the method provided in this paper, one can assign the rightmost eigenvalues of ...

For a linear time-invariant system with a feedback controller, the closed-loop eigenvalues perturb due to system uncertainties. Given an allowable tolerance for the closed-loop eigenvalue perturbation, an algorithm is developed to obtain a state feedback controller that maximizes the uncertainty tolerance of the open-loop system matrix. The design procedure is based on an existing eigenvalue as...

Wind power is seen as the most cost effective way to generate electricity from renewable sources. The wind turbine prime mover, wind, is uncontrollable as compared to the conventional power plant prime mover. Therefore, it becomes very important to carry out investigations on the dynamic behavior of wind power generating systems. In this paper, the dynamic model of 1 MVA unit is extrapolated fr...

3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . ...

An approach for eigenvalue assignment in linear descriptor systems via output feedback is proposed. Sufficient conditions in order that a given set of eigenvalues is assignable are established. Parametric form of the desired output feedback gain matrix is also given. The approach assigns the full number of generalised eigenvalues, guarantees the closed-loop regularity and overcomes the defects ...