A stability condition for certain bilinear systems

Journal ArticleAbstract-This correspondence derives a simple sufficient condition for the output of a discrete-time, time-invariant bilinear system to be bounded whenever the input signal to the system is bounded by a finite constant

Type II balanced truncation for deterministic bilinear control systems

When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce computational complexity. A particular MOR technique to obtain a reduced order model (ROM) is balanced truncation (BT), a method which has been extensively studied for deterministic linear systems. As so-called type I BT it has already been extended to bilinear equations, an important subclass of nonlinear systems. We provide an alternative generalisation of the linear setting to bilinear systems which is called type II BT. The Gramians that we propose in this context contain information about the control. It turns out that the new approach delivers energy bounds which are not just valid in a small neighbourhood of zero. Furthermore, we provide an $H_\infty$-error bound which so far is not known when applying type I BT to bilinear systems

D-brane categories

This is an exposition of recent progress in the categorical approach to D-brane physics. I discuss the physical underpinnings of the appearance of homotopy categories and triangulated categories of D-branes from a string field theoretic perspective, and with a focus on applications to homological mirror symmetry.Comment: 37 pages, IJMPA styl

On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulatio

Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping

We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at one boundary. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the opposite boundary. We first prove that the linearized and nonlinear unforced systems are well-posed and exponentially stable under certain conditions on the damping parameters, and then consider a balanced truncation method to generate the reduced order model (ROM) of the nonlinear input-output system. Little is known about model reduction of nonlinear input-output systems, and so we present detailed numerical experiments concerning the performance of the nonlinear ROM. We find that the ROM is accurate for many different combinations of model parameters