On robust control of continuous-time systems with state-dependent uncertainties and its application to mechanical systems

•A more general polytopic model describing systems with state-dependent uncertain parameters is proposed, and such a system model is more applicable in practice.•By introducing the Lagrange multiplier term and adding some weight matrix variables, some improved results are given for our considered system.•The results of the paper will successfully solve the robust stabilization of continuous-time systems with state-dependent uncertainties.•The results have the advantages of low conservativeness, and more applicability, and a decay rate can be set in advance to achieve better system performances.

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.