Computational issues in fault detection filter design

We discuss computational issues encountered in the design of residual generators for dynamic inversion based fault detection filters. The two main computational problems in determining a proper and stable residual generator are the computation of an appropriate leftinverse of the fault-system and the computation of coprime factorizations with proper and stable factors. We discuss numerically reliable approaches for both of these computations relying on matrix pencil approaches and recursive pole assignment techniques for descriptor systems. The proposed computational approach to design fault detection filters is completely general and can easily handle even unstable and/or improper systems

An efficient projector-based passivity test for descriptor systems

An efficient passivity test based on canonical projector techniques is proposed for descriptor systems (DSs) widely encountered in circuit and system modeling. The test features a natural flow that first evaluates the index of a DS, followed by possible decoupling into its proper and improper subsystems. Explicit state-space formulations for respective subsystems are derived to facilitate further processing such as model order reduction and/or passivity enforcement. Efficient projector construction and a fast generalized Hamiltonian test for the proper-part passivity are also elaborated. Numerical examples then confirm the superiority of the proposed method over existing passivity tests for DSs based on linear matrix inequalities or skew-Hamiltonian/Hamiltonian matrix pencils. © 2010 IEEE.published_or_final_versio

Linear Control Theory with an ℋ∞ Optimality Criterion

This expository paper sets out the principal results in ℋ∞ control theory in the context of continuous-time linear systems. The focus is on the mathematical theory rather than computational methods

PEDS: Passivity enforcement for descriptor systems via Hamiltonian- symplectic matrix pencil perturbation

Passivity is a crucial property of macromodels to guarantee stable global (interconnected) simulation. However, weakly nonpassive models may be generated for passive circuits and systems in various contexts, such as data fitting, model order reduction (MOR) and electromagnetic (EM) macromodeling. Therefore, a post-processing passivity enforcement algorithm is desired. Most existing algorithms are designed to handle poleresidue models. The few algorithms for state space models only handle regular systems (RSs) with a nonsingular D+D T term. To the authors' best knowledge, no algorithm has been proposed to enforce passivity for more general descriptor systems (DSs) and state space models with singular D + D T terms. In this paper, a new post-processing passivity enforcement algorithm based on perturbation of Hamiltonian-symplectic matrix pencil, PEDS, is proposed. PEDS, for the first time, can enforce passivity for DSs. It can also handle all kinds of state space models (both RSs and DSs) with singular D + D T terms. Moreover, a criterion to control the error of perturbation is devised, with which the optimal passive models with the best accuracy can be obtained. Numerical examples then verify that PEDS is efficient, robust and relatively cheap for passivity enforcement of DSs with mild passivity violations. ©2010 IEEE.published_or_final_versionThe IEEE/ACM International Conference on Computer-Aided Design (ICCAD 2010), San Jose, CA., 7-11 November 2010. In Proceedings of ICCAD, 2010, p. 800-80

Passivity enforcement for descriptor systems via matrix pencil perturbation

Passivity is an important property of circuits and systems to guarantee stable global simulation. Nonetheless, nonpassive models may result from passive underlying structures due to numerical or measurement error/inaccuracy. A postprocessing passivity enforcement algorithm is therefore desirable to perturb the model to be passive under a controlled error. However, previous literature only reports such passivity enforcement algorithms for pole-residue models and regular systems (RSs). In this paper, passivity enforcement algorithms for descriptor systems (DSs, a superset of RSs) with possibly singular direct term (specifically, D+D T or I-DD T) are proposed. The proposed algorithms cover all kinds of state-space models (RSs or DSs, with direct terms being singular or nonsingular, in the immittance or scattering representation) and thus have a much wider application scope than existing algorithms. The passivity enforcement is reduced to two standard optimization problems that can be solved efficiently. The objective functions in both optimization problems are the error functions, hence perturbed models with adequate accuracy can be obtained. Numerical examples then verify the efficiency and robustness of the proposed algorithms. © 2012 IEEE.published_or_final_versio

The Minimal Modal Interpretation of Quantum Theory

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture of states and Hilbert-space trajectories to the case of open quantum systems as well. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure---which we call subsystem space---that we believe merits further study. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text.Comment: 73 pages + references, 9 figures; cosmetic changes, added figure, updated references, generalized conditional probabilities with attendant changes to the sections on the EPR-Bohm thought experiment and Lorentz invariance; for a concise summary, see the companion letter at arXiv:1405.675

Periodic Ising Correlations

In this paper, we first rework B. Kaufman's 1949 paper, "Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis", by using representation theory. Our approach leads to a simpler and more direct way of deriving the spectrum of the transfer matrix for the finite periodic Ising model. We then determine formulas for the spin correlation functions that depend on the matrix elements of the induced rotation associated with the spin operator in a basis of eigenvectors for the transfer matrix. The representation of the spin matrix elements is obtained by considering the spin operator as an intertwining map. We exhibit the "new" elements V+ and V- in the Bugrij-Lisovyy formula as part of a holomorphic factorization of the periodic and anti-periodic summability kernels on the spectral curve associated with the induced rotation for the transfer matrix.Comment: 36 page