Algebraic methods for the solution of some linear matrix equations

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method

Exact solution of some linear matrix equations using algebraic methods

A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given

Control optimization, stabilization and computer algorithms for aircraft applications

Computationally useful algorithms are considered that can aid the control engineer in designing systems control in linear time invariant dynamics for aircraft applications. Structural aspects of system identification, matrix parameterization, and the effect of feedback on identifiability of systems. Adaptive and stochastic control model constructions are projected, and a method for approximate identification of aircraft characteristics and subsequent generation of control signals is outlined

A note on stochastic dissipativeness

In this paper we present a stochastic version of Willems'ideas on Dissipativity and generalize the dissipation inequality to Markov Diffusion Processes. We show the relevance of these ideas by examining the problem of Ergodic Control of partially observed diffusions

Renormalization of the Hamiltonian and a geometric interpretation of asymptotic freedom

Using a novel approach to renormalization in the Hamiltonian formalism, we study the connection between asymptotic freedom and the renormalization group flow of the configuration space metric. It is argued that in asymptotically free theories the effective distance between configuration decreases as high momentum modes are integrated out.Comment: 22 pages, LaTeX, no figures; final version accepted in Phys.Rev.D; added reference and appendix with comment on solution of eq. (9) in the tex

Modern ‘live’ football: moving from the panoptican gaze to the performative, virtual and carnivalesque

Drawing on Redhead's discussion of Baudrillard as a theorist of hyperreality, the paper considers the different ways in which the mediatized ‘live’ football spectacle is often modelled on the ‘live’ however eventually usurps the ‘live’ forms position in the cultural economy, thus beginning to replicate the mediatized ‘live’. The blurring of the ‘live’ and ‘real’ through an accelerated mediatization of football allows the formation of an imagined community mobilized by the working class whilst mediated through the sanitization, selling of ‘events’ and the middle classing of football, through the re-encoding of sporting spaces and strategic decision-making about broadcasting. A culture of pub supporting then allows potential for working-class supporters to remove themselves from the panoptican gazing systems of late modern hyperreal football stadia and into carnivalesque performative spaces, which in many cases are hyperreal and simulated themselves

Completeness of Wilson loop functionals on the moduli space of SL(2,C)SL(2,C) and SU(1,1)SU(1,1)-connections

The structure of the moduli spaces \M := \A/\G of (all, not just flat) $SL(2,C)$ and $SU(1,1)$ connections on a n-manifold is analysed. For any topology on the corresponding spaces \A of all connections which satisfies the weak requirement of compatibility with the affine structure of \A, the moduli space \M is shown to be non-Hausdorff. It is then shown that the Wilson loop functionals --i.e., the traces of holonomies of connections around closed loops-- are complete in the sense that they suffice to separate all separable points of \M. The methods are general enough to allow the underlying n-manifold to be topologically non-trivial and for connections to be defined on non-trivial bundles. The results have implications for canonical quantum general relativity in 4 and 3 dimensions.Comment: Plain TeX, 7 pages, SU-GP-93/4-

Confidence and Backaction in the Quantum Filter Equation

We study the confidence and backaction of state reconstruction based on a continuous weak measurement and the quantum filter equation. As a physical example we use the traditional model of a double quantum dot being continuously monitored by a quantum point contact. We examine the confidence of the estimate of a state constructed from the measurement record, and the effect of backaction of that measurement on that state. Finally, in the case of general measurements we show that using the relative entropy as a measure of confidence allows us to define the lower bound on the confidence as a type of quantum discord.Comment: 9 pages, 6 figure