Dissipative state observer design for nonlinear time-delay systems |
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| Institution: | 1. Universidad Autónoma de Baja California, Facultad de Ciencias de la Ingeniería, Administrativas y Sociales, Tecate, C.P. 21460, Baja California, Mexico;2. Universidad Nacional Autónoma de México, Instituto de Ingeniería, Coyoacán, Ciudad de México, C.P. 04510, Mexico;3. Instituto Politécnico Nacional, Sección de Estudios de Investigación y Posgrado, ESIME-UPT, Ciudad de México, C.P. 07430, Mexico;1. College of Information Engineering, Henan University science and technology, Luoyang 471023, PR China;2. School of Marine Engineering, Dalian Maritime University, Dalian 116026, China;1. School of Information Engineering, Henan University of Science and Technology, Luoyang 471023, P.R. China;2. Department of Automatic Control, Robotics and Fluid Technique, Faculty of Mechanical and Civil Engineering, University of Kragujevac, 36000 Kraljevo, Serbia;1. Federal Rural University of the Semi-Arid Region, Rua Francisco Mota, 572, Pres. Costa e Silva, Mossoró, 59625-900, RN, Brazil;2. São Paulo State University, Avenida Brasil, 56, Centro, Ilha Solteira, 15385-000, SP, Brazil;3. Goiás Federal Institute of Education, Science, and Technology, Av. Presidente Juscelino Kubitschek, 775, Residencial Flamboyant, Jataí, 75804-714, GO, Brazil;1. Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, PR China;2. Key Laboratory of System Control and Information Process, Ministry of Education, Shanghai 200240, PR China;3. Department of Mechnical Engineering, Politecnico di Milano, Milan 20156, Italy;1. School of Automation, Central South University, Changsha, Hunan 410083, China;2. Industrial Mathematics Lab of Baikal School of BRICS, Irkutsk National Research Technical University, Lermontov Str.83, Irkutsk 664074, Russia;1. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, Shandong, 266520, China;2. School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong, 252059, China;3. School of Automation, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, 210044, China |
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| Abstract: | This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results. |
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