Stabilisation of time-varying linear systems via Lyapunov differential equations |
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Authors: | Bin Zhou Guang-Bin Cai Guang-Ren Duan |
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Affiliation: | 1. Center for Control Theory and Guidance Technology , Harbin Institute of Technology , Harbin 150001 , P.R. China binzhoulee@163.com binzhou@hit.edu.cn;3. Department of Automation , Xi'an Research Institute of High-Tech , Hongqing Town, Xi'an , Shaanxi 710025 , P.R. China;4. Center for Control Theory and Guidance Technology , Harbin Institute of Technology , Harbin 150001 , P.R. China |
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Abstract: | This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open-loop system is exactly known, or the future information of the system matrices are accessible in advance. Different from the first class of controllers which may be difficult to implement in practice, the second type of controllers can be easily implemented by solving a state-dependent Lyapunov differential equation with a given positive-definite initial condition. In both cases, explicit conditions are obtained to guarantee the exponentially asymptotic stability of the associated closed-loop systems. Numerical examples show the effectiveness of the proposed approaches. |
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Keywords: | time-varying linear systems Lyapunov differential equation exponentially asymptotic stability stabilisation |
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