The tracking problem for continuous-time systems is investigated. It is assumed that the states of the systems are not available. An observer is firstly designed to estimate the states by using the H∞ method. The control action is consist of a state-feedback control, an integral component, and a feedforward loop. The linear-matrix-inequality region is used to constrain the eigenvalue location f...

In this paper, the authors present a linear matrix inequality (LMI) approach to the strictly positive real (SPR) synthesis problem: find an output feedback K such that the closed-loop system T (s) is SPR. The authors establish that if no such constant output feedback K exists, then no dynamic output feedback with a proper transfer matrix exists to make the closed-loop system SPR. The existence ...

We describe an iterative scheme which allows us to calculate any multi-loop corre-lator for the complex matrix model to any genus using only the first in the chain of loop equations. The method works for a completely general potential and the results contain no explicit reference to the couplings. The genus g contribution to the m–loop correlator depends on a finite number of parameters, namely...

Efficient implementation of matrix algebra is important to the performance of many large and complex physical models. Among important tuning techniques is loop fusion which can reduce the amount of data moved between memory and the processor. We have developed the Build to Order (BTO) compiler to automate loop fusion for matrix algebra kernels. In this paper, we present BTO’s analytic memory mo...

The phase diagram of the O(n) model, in particular the special case n = 0, is studied by means of transfer-matrix calculations on the loop representation of the O(n) model. The model is defined on the square lattice; the loops are allowed to collide at the lattice vertices, but not to intersect. The loop model contains three variable parameters that determine the loop density or temperature, th...

We study bubbling geometry in topological string theory. Specifically, we analyse ChernSimons theory on both the 3-sphere and lens spaces in the presence of a Wilson loop of an arbitrary representation. For each three manifold, we formulate a multi-matrix model whose partition function is the Wilson loop vev and compute the spectral curve. This spectral curve is closely related to the Calabi-Ya...