Open AccessAn Error Bound for Low Order Approximation of Dynamical Systems Subjected to Initial Conditions
Author(s) -
Gabriel Pedro Ramos Maciel,
Roberto Spínola Barbosa
Publication year - 2018
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2018.019.02.197
Subject(s) - unitary state , upper and lower bounds , norm (philosophy) , dynamical systems theory , approximation error , control theory (sociology) , linear dynamical system , mathematics , order (exchange) , computer science , controller (irrigation) , linear system , physics , control (management) , mathematical analysis , quantum mechanics , agronomy , finance , artificial intelligence , political science , law , economics , biology
In recent years, a great effort has been taken focused on the development of reduced order modeling techniques of dynamical systems. This necessity is pushed by the requirement for efficient numerical techniques for simulations of dynamical systems arising from structural dynamics, controller design, circuit simulation, fluid dynamics and micro electromechanical systems.We introduce a method to calculate the minimum upper $\mathcal{L}_2$ error bound of a linear time invaritant reduced order model considering any possible unitary initial conditions (IC). As a consequence, the proposed method calculates the unitary IC vector which leads to the maximum $\mathcal{L}_2$ norm of the error. Based on this error bound, it is discussed the capacity of a reduced order system to approximate the free transient response in the worst case scenario.