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We present a numerical method to analyse the relative stability of closed-loop single-input–single-output (SISO) dead-time systems on a given left complex half-plane for all positive delays. The well-known boundary crossing method for the imaginary axis is extended to a given vertical line stability boundary in the complex plane for these types of systems. The method allows us to compute the characteristic roots crossing the relative stability boundary and their corresponding delays up to a maximum predefined delay. Based on this method, we analyse the relative stability of the closed-loop system for all positive delays. Both numerical methods are effective for high-order SISO dead-time systems. [ABSTRACT FROM AUTHOR]

Abstract: We present a numerical method to plot the root locus of Single-Input–Single-Output (SISO) dead-time systems with respect to the controller gain or the system delay. We compute the trajectories of characteristic roots of the closed-loop system on a prescribed complex right half-plane. We calculate the starting, branch and boundary crossing roots of root-locus branches inside the region. We compute the root locus of each characteristic root based on a predictor–corrector type continuation method. To avoid the high sensitivity of roots with respect to the locus parameter in the neighborhood of branch points, the continuation method relies on a natural parameterization of the root-locus trajectory in terms of a distance in the (characteristic root, locus parameter)-space. The method is numerically stable for high order SISO dead-time systems. [Copyright &y& Elsevier]

We analyze and design H-infinity controllers for general time-delay systems with time-delays in systems' state, inputs, and outputs. We allow the designer to choose the order of the controller and to introduce constant time-delays into the controller. The closed-loop system of the plant and the controller is modeled by a system of delay differential algebraic equations (DDAEs). The advantage of the DDAE modeling framework is that any interconnection of systems and controllers prone to various types of delays can be dealt with in a systematic way, without using any elimination technique. We present a predictor-corrector algorithm for the H-infinity norm computation of systems described by DDAEs. Instrumental to this we analyze the properties of the H-infinity norm. In particular, we illustrate that it may be sensitive with respect to arbitrarily small delay perturbations. Due to this sensitivity, we introduce the strong H-infinity norm, which explicitly takes into account small delay perturbations, inevitable in any practical control application. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs. Using this algorithm and the computation of the gradient of the strong H-infinity norm with respect to the controller parameters, we minimize the strong H-infinity norm of the closed-loop system based on nonsmooth, nonconvex optimization methods. By this approach, we tune the controller parameters and design H-infinity controllers with a prescribed order or structure. [ABSTRACT FROM AUTHOR]

We consider the characterization and computation of H∞ norms for a class of time-delay systems. It is well known that in the finite-dimensional case the H∞ norm of a transfer function can be computed using the connections between the corresponding singular value curves and the imaginary axis eigenvalues of a Hamiltonian matrix, leading to the established level set methods. We show a similar connection between the transfer function of a time-delay system and the imaginary axis eigenvalues of an infinite-dimensional linear operator Lξ. Based on this result, we propose a predictor-corrector algorithm for the computation of the H∞ norm. In the prediction step, a finite-dimensional approximation of the problem, induced by a spectral discretization of the operator Lξ, and an adaptation of the algorithms for finite-dimensional systems, allow us to obtain an approximation of the H∞ norm of the transfer function of the time-delay system. In the next step the approximate results are corrected to the desired accuracy by solving a set of nonlinear equations which are obtained from the reformulation of the eigenvalue problem for the linear infinite-dimensional operator Lξ as a finite-dimensional nonlinear eigenvalue problem. These equations can be interpreted as characterizations of peak values in the singular value plot. The effects of the discretization in the predictor step are fully characterized, and the choice of the number of discretization points is discussed. The paper concludes with a numerical example and the presentation of the results of extensive benchmarking. [ABSTRACT FROM AUTHOR]

Abstract: The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound. The pseudospectral abscissa is defined as the maximum real part of the characteristic roots in the pseudospectrum and, therefore, it is for instance important from a robust stability point of view. In this paper we present an accurate method for the computation of the pseudospectral abscissa of retarded delay differential equations with discrete pointwise delays. Our approach is based on the connections between the pseudospectrum and the level sets of an appropriately defined complex function. The computation is done in two steps. In the prediction step, an approximation of the pseudospectral is obtained based on a rational approximation of the characteristic matrix and the application of a bisection algorithm. Each step in this bisection algorithm relies on checking the presence of the imaginary axis eigenvalues of a complex matrix, similar to the delay free case. In the corrector step, the approximate pseudospectral abscissa is corrected to any given accuracy, by solving a set of nonlinear equations that characterizes the extreme points in the pseudospectrum contours. [Copyright &y& Elsevier]

Approximately 18 percent of the 3.2 million smartphone applications rely on integrated graphics processing units (GPUs) to achieve competitive performance. Graphics performance, typically measured in frames per second, is a strong function of the GPU frequency, which in turn has a significant impact on mobile processor power consumption. Consequently, dynamic power management algorithms have to assess the performance sensitivity to the frequency accurately to choose the operating frequency of the GPU effectively. Since the impact of GPU frequency on performance varies rapidly over time, there is a need for online performance models that can adapt to varying workloads. This paper presents a light-weight adaptive runtime performance model that predicts the frame processing time of graphics workloads at runtime without apriori characterization. We employ this model to estimate the frame time sensitivity to the GPU frequency, i.e., the partial derivative of the frame time with respect to the GPU frequency. The proposed model does not rely on any parameter learned offline. Our experiments on commercial platforms with common GPU benchmarks show that the mean absolute percentage error in frame time and frame time sensitivity prediction are 4.2 and 6.7 percent, respectively. [ABSTRACT FROM AUTHOR]