Sökning: "Lyapunov equation"

Visar resultat 1 - 5 av 6 avhandlingar innehållade orden Lyapunov equation.

1. 1. Approximating Stochastic Partial Differential Equations with Finite Elements: Computation and Analysis

   Författare :Andreas Petersson; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Lévy process; Lyapunov equation; white noise; finite element method; multilevel Monte Carlo; Monte Carlo; multiplicative noise; asymptotic mean square stability; stochastic heat equation; covariance operator; weak convergence; generalized Wiener process; numerical approximation; stochastic wave equation; Stochastic partial differential equations;

   Sammanfattning : Stochastic partial differential equations (SPDE) must be approximated in space and time to allow for the simulation of their solutions. In this thesis fully discrete approximations of such equations are considered, with an emphasis on finite element methods combined with rational semigroup approximations. LÄS MER

3. 2. Numerical methods for Sylvester-type matrix equations and nonlinear eigenvalue problems

   Författare :Emil Ringh; Elias Jarlebring; Johan Karlsson; Per Enqvist; Daniel Kressner; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Matrix equations; Lyapunov equation; Sylvester equation; nonlinear eigenvalue problems; two-parameter eigenvalue problems; Krylov methods; iterative methods; preconditioning; projection methods; Matrisekvationer; Lyapunovekvationen; Sylvesterekvationen; ickelinjära egenvärdesproblem; två-parameters egenvärdesproblem; Krylovmetoder; iterativa metoder; förkonditionering; projektionsmetoder; Tillämpad matematik och beräkningsmatematik; Applied and Computational Mathematics; Optimization and Systems Theory; Optimeringslära och systemteori; Numerical Analysis; Numerisk analys;

   Sammanfattning : Linear matrix equations and nonlinear eigenvalue problems (NEP) appear in a wide variety of applications in science and engineering. Important special cases of the former are the Lyapunov equation, the Sylvester equation, and their respective generalizations. These appear, e.g. LÄS MER

4. 3. Control and Analysis of Pulse-Modulated Systems

   Författare :Stefan Almér; Ulf Jönsson; Gilead Tadmor; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Pulse-width modulation; Periodic systems; Stability analysis; Harmonic analysis; Lyapunov methods; Dynamic phasors; Harmonic transfer function; Switched mode power converters; Sampled data modeling; H-infinity synthesis; Optimization; systems theory; Optimeringslära; systemteori;

   Sammanfattning : The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. LÄS MER

5. 4. A Certain Class of Foster-Lyapunov Functions and Ergodic Properties for Markov Models

   Författare :Marina Tsygan; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : Let be a homogeneous Markov chain with state space , and let be the root of the equation and define . Using or close modifications of as test function in Foster's criteria, conditions for recurrence / geometrically recurrence / transience / ergodicity / null recurrence are developed. LÄS MER

7. 5. Constructive Commutative Algebra in Nonlinear Control Theory

   Författare :Krister Forsman; Linköpings universitet; []
   Nyckelord :TEKNIK OCH TEKNOLOGIER; ENGINEERING AND TECHNOLOGY;

   Sammanfattning : This thesis consists of two parts. The first part is a short review of those results from commutative algebra, algebraic geometry and differential algebra that are needed in this work. The emphasis is on constructive methods. The second part contains applications of these methods to topics in control theory, mainly nonlinear systems. LÄS MER