title: On robust control of continuous-time systems with state-dependent uncertainties and its application to mechanical systems.
abstract: This paper revisits the problems of robust stability analysis and control of continuous-time systems with state-dependent uncertainties. First, a more general polytopic model describing systems with state-dependent uncertain parameters is proposed, and such a system model is more applicable in practice. A low conservative stability condition is obtained for the system by introducing the Lagrange multiplier term and adding some weight matrix variables. Then, based on our proposed idea, the output-feedback controllers will be designed in two cases: (1) the system matrices share the same polytopic parameters; (2) the system matrices do not share the same polytopic parameters. The controllers are designed in a model-dependent manner, which can provide more flexibilities in control synthesis. Besides, a decay rate can be set in advance to achieve better system performances. Finally, a numerical example together with a classic mechanical system is used to demonstrate the effectiveness and applicability of our theoretical findings.
authors.affiliation: Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China. Electronic address: zhengchaohit@gmail.com.
authors.forename: Zhengchao
authors.initials: Z
authors.lastname: Li
authors.affiliation: College of Engineering, Bohai University, Jinzhou 121013, China. Electronic address: xdzhaohit@gmail.com.
authors.forename: Xudong
authors.initials: X
authors.lastname: Zhao
authors.affiliation: Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China. Electronic address: yujinyong.hit@gmail.com.
authors.forename: Jinyong
authors.initials: J
authors.lastname: Yu
keywords: Lyapunov function approach; Mechanical systems; Robust control; State-dependent; Uncertainties