## RELATIVE ERROR CONTROL IN QUANTIZATION BASED INTEGRATION

Citations: | 5 - 1 self |

### BibTeX

@MISC{Kofman_relativeerror,

author = {Ernesto Kofman},

title = {RELATIVE ERROR CONTROL IN QUANTIZATION BASED INTEGRATION},

year = {}

}

### OpenURL

### Abstract

Abstract — This paper introduces a method to achieve reltive error control in Quantized State System (QSS) methods. Based on the use of logarithmic quantization, the proposed methodology solves the problem of quantum selection.

### Citations

358 |
Solving ordinary differential equations. I: Nonstiff problems
- Hairer, Nørsett, et al.
- 1987
(Show Context)
Citation Context ...ment. Based on classic methods like Euler, Runge–Kutta and Adams and impulsed with the development of modern and fast computers, several variable–step and implicit ODE solver methods were introduced (=-=Hairer et al., 1993-=-; Hairer and Wanner, 1991; Cellier and Kofman, 2006). Simultaneously, different software simulation tools implementing those modern methods have been developed. Matlab/Simulink (Shampine and Reichelt,... |

45 |
Continuous System Simulation
- Cellier, Kofman
- 2006
(Show Context)
Citation Context ...ge–Kutta and Adams and impulsed with the development of modern and fast computers, several variable–step and implicit ODE solver methods were introduced (Hairer et al., 1993; Hairer and Wanner, 1991; =-=Cellier and Kofman, 2006-=-). Simultaneously, different software simulation tools implementing those modern methods have been developed. Matlab/Simulink (Shampine and Reichelt, 1997) and Dymola (Elmqvist et al., 1995) can be me... |

38 | Discrete event simulation of hybrid systems
- Kofman
- 2004
(Show Context)
Citation Context ...), and a first order Centered QSS for marginally stable systems. The QSS–methods show some important advantages with respect to classic discrete time methods in the integration of discontinuous ODEs (=-=Kofman, 2004-=-), sparsity exploitation (Kofman, 2002), explicit integration of stiff and marginally stable systems (Migoni et al., 2007), absolute stability, and the existence of a global error bound (Cellier and K... |

11 |
A systematic method to obtain ultimate bounds for perturbed systems
- Kofman, Haimovich, et al.
(Show Context)
Citation Context ...order to prove this property, we need first to study the effects of delayed–affine perturbations in a generic LTI system. A. Ultimate Bound with Affine Perturbations The following theorem, proven in (=-=Kofman et al., 2007-=-), is an auxiliary result for the main result of this section. Theorem 1. Consider the system ˙e(t) = Ae(t) + Hw(t) (8) where e(t) ∈ R n , w(t) ∈ R k , H ∈ R n×k and A ∈ R n×n is a Hurwitz matrix with... |

10 |
A third order discrete event simulation method for continuous system simulation
- Kofman
(Show Context)
Citation Context ... Adams and impulsed with the development of modern and fast computers, several variable–step and implicit ODE solver methods were introduced (Hairer et al., 1993; Hairer and Wanner, 1991; Cellier and =-=Kofman, 2006-=-). Simultaneously, different software simulation tools implementing those modern methods have been developed. Matlab/Simulink (Shampine and Reichelt, 1997) and Dymola (Elmqvist et al., 1995) can be me... |

5 |
A Second Order Approximation for DEVS
- Kofman
(Show Context)
Citation Context ...ely fast oscillations– and formalized as the Quantized State Systems (QSS) method for ODE integration in (Kofman and Junco, 2001). This was followed by the definition of the second order QSS2 method (=-=Kofman, 2002-=-), the third order QSS3 method (Kofman, 2006), a first order Backward QSS method (BQSS) for stiff systems (Migoni et al., 2007), and a first order Centered QSS for marginally stable systems. The QSS–m... |

5 |
Simulación por Cuantificación de Sistemas Stiff, Ph.D. Thesis, Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de
- Migoni
- 2010
(Show Context)
Citation Context ...nco, 2001). This was followed by the definition of the second order QSS2 method (Kofman, 2002), the third order QSS3 method (Kofman, 2006), a first order Backward QSS method (BQSS) for stiff systems (=-=Migoni et al., 2007-=-), and a first order Centered QSS for marginally stable systems. The QSS–methods show some important advantages with respect to classic discrete time methods in the integration of discontinuous ODEs (... |

3 |
Control design with guaranteed ultimate bound for perturbed systems
- Kofman, Seron, et al.
(Show Context)
Citation Context ...ate bound for a LTI system with perturbations bounded by an affine delayed function of the state. Particularly, it shows the invariance property of the ultimate bound set estimated by Theorem 3.1 of (=-=Kofman et al., 2008-=-).Theorem 2. Consider the perturbed system ˙e(t) = Ae(t) + Hw(t), (10) where e(t) ∈ R n , A ∈ R n×n is a Hurwitz matrix with Jordan canonical form Λ = V −1 AV , H ∈ R n×k and the perturbation variabl... |

1 | Una Herramienta Integrada de Simulación por Eventos Discretos - Pagliero, Lapadula, et al. - 2003 |