Logarithmic matrix norms in motion stability problems |
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| Authors: | OA Peregudova |
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| Institution: | 1. College of Automation, Huazhong University of Science and Technology, Wuhan 430074, PR China;2. Key Laboratory of Image Information Processing and Intelligent Control (Huazhong University of Science and Technology), Ministry of Education, Wuhan 430074, PR China;3. School of Science, Hubei University of Technology, Wuhan 430068, PR China;4. School of Electronics and Information, Yangtze University, Jingzhou 434023, PR China;5. College of Mechatronics and Control Engineering, Hubei Normal University, Huangshi 435002, PR China;1. College of Electronic and Information Engineering, Southwest University, Chongqing 400715, China;2. Department of Mathematics, Texas A&M University at Qatar, Doha 23874, Qatar;1. The State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China;2. The Department of Mechanical and Industrial Engineering, Concordia University, Montreal, QC, Canada H3G 1M8;3. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China |
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| Abstract: | The problem of the stability of the motions of mechanical systems, described by non-linear non-autonomous systems of ordinary differential equations, is considered. Using the logarithmic matrix norm method, and constructing a reference system, the sufficient conditions for the asymptotic and exponential stability of unperturbed motion and for the stabilization of progammed motions of such systems are obtained. The problem of the asymptotic stability of a non-conservative system with two degrees of freedom is solved, taking for parametric disturbances into account. Examples of the solution of the problem of stabilizing programmed motions – for an inverted double pendulum and for a two-link manipulator on a stationary base – are considered. |
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