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

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.