This paper presents a simple, but effective, design method for decentralized PI control systems with guaranteed closed-loop stability. Nyquist stability conditions are used to derive the stability region for each PI controller in terms of the controller parameters. A detuning factor for each loop is specified based on a diagonal dominance index. Then appropriate controller settings are determin...

24 restriction. As and , the minimum of δ (l) is achieved on the boundary of R. It is not difficult to see that this minimum is in x = y = , independently of the values of the greek letters. With this, we can see that: Now, if , we have: which allows to finish the proof: x y , () R ∈ 0 δ l 1 − () 1 − , [ ] 0 δ l 1 − () 1 − , [ ] × = x ∂ ∂δ l () 0 ≠ y ∂ ∂δ l () 0 ≠ δ l 1 − () 1 − δ l () δ l 1 − ...

Let A be a matrix such that the diagonal matrix D with the same diagonal as A is invertible. It is well known that if (1) A satisfies the Sassenfeld condition then its Gauss-Seidel scheme is convergent, and (2) if D−1A certifies certain classical diagonal dominance conditions then the Jacobi iterations for A are convergent. In this paper we generalize the second result and extend the first resu...

A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a stable solution. The algorithm is shown to be stable for block diagonally dominant matrices and for M-matrices.

The Rectangular Land Survey, which covers 69 percent of the Unites States continuously, was a system of federal land management that began in 1785 and continued into the early twentieth century. Straight, gridded patterns were stretched across the country in an attempt to make the consolidation and distribution of land by the United States government quick and easy. Using the Dominant Ideology ...

Discrete nonnegativity principles are established for finite element approximations of nonlinear parabolic PDE systems with mixed boundary conditions. Previous results of the authors are extended such that diagonal dominance (or essentially monotonicity) of the nonlinear coupling can be relaxed, allowing to include much more general situations in suitable models.

In this paper we investigate power allocation and crosstalk cancellation for MIMO-DSL (a.k.a. bonded-DSL) systems. Exploiting a property of the DSL channel, namely columnwise diagonal dominance, allows us to simplify the power allocation and crosstalk cancellation problems. This leads to a significant reduction in initialisation and run-time complexity whilst maintaining near-optimal performanc...

It is known that interpolation with radial basis functions of the same shape can guarantee a non-singular interpolation matrix, whereas little is known when one uses various shapes. In this paper, we prove that a class of compactly supported radial basis functions are convex on a certain region; based on this local convexity and ready local geometrical property of the interpolation points, we c...

We dedicate this paper to Professor Ron Mitchell who has been an inspiration to many generations of numerical analysts. In addition his generous spirit has infused our discipline with a sense of positive endeavour. We examine whether three diierent upwind schemes for the positive definite advection diiusion problem can yield indeenite coeecient matrices. In particular, in line with the increasi...

The problem of computing the frequency response of linear systems with parametric perturbation is addressed. Under the assumption that the coefficients of the system transfer function depend on the perturbation parameters in a linear manner, we provide results for plotting the frequency response of the perturbed transfer function. These results are useful in determining the H~ norm, gain margin...