A method of continuous time approximation of delayed dynamical systems |
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| Authors: | Jian-Qiao Sun |
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| Institution: | 1. Opening Project of Key Laboratory of Mine Informatization, Henan Polytechnic University, Jiaozuo 454000, China;2. School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China;1. IDMEC-Polo FEUP, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias 404, 4200-465 Porto, Portugal;2. LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal;3. ISEL, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal;4. Faculdade de Engenharia da Universidade do Porto, Universidade do Porto, Rua Dr. Roberto Frias 404, 4200-465 Porto, Portugal;5. Department of Mathematics, Faculty of Science, King Abdulaziz University Jeddah, Saudi Arabia |
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| Abstract: | This paper presents a new method to analyze response of linear and nonlinear dynamical systems with time delay. The method proposes a continuous time approximation of the delayed portion of the response. This leads to a high and finite dimensional state space formulation of the time-delayed system. The advantage of the current method lies in that the resulting finite dimensional state equations are in the standard state space form, making all the existing analysis methods and control design tools for linear and nonlinear dynamical systems amenable to the current approach. The method can also handle multiple independent time delays in a natural way. One- and two-dimensional dynamical systems with time delay are used to demonstrate the effectiveness of the method. |
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