On hyper-exponential stability and stabilization of linear systems by bounded linear time-varying controllers |
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| Affiliation: | 1. Department of Electrical and Computer Engineering, University of Alberta, Edmonton T6G 2W3, Canada;2. Department of Electrical Engineering, Sahand University of Technology, Tabriz, Iran;1. Department of Electrical Engineering, University of Technology of Paraná – UTFPR Cornélio Procópio 86300-000, PR, Brazil;2. Federal Institute of São Paulo – IFSP, Campus Avaré, Avaré 18707-150, SP, Brazil;1. College of Information Engineering, Nanjing University of Finance and Economics, Nanjing 210023, China;2. CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China;3. NARI Group Corporation (State Grid Electric Power Research Institute), Nanjing 211106, China |
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| Abstract: | Hyper-exponential stability analysis and hyper-exponential stabilization of linear systems by bounded linear time-varying feedback are investigated in this paper. On the one hand, we propose some Lyapunov-like hyper-exponential stability theorems (both global and local) based on the comparison principle and the concepts of hyper-exponentially stable functions and hyper-exponentially increasing functions. On the other hand, we establish methods to design bounded linear time-varying controllers such that hyper-exponential stability of linear time-invariant systems can be guaranteed. The key design tool is the utilization of a time-varying parameter contained in the controller and the properties of solution to a parametric Lyapunov equation. Both state feedback and observer-based output feedback are accommodated. As a further result, hyper-exponential semi-global stabilization for linear systems by bounded controls is discussed. Finally, the validity of the proposed schemes is illustrated through numerical simulations on spacecraft rendezvous control system. |
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