混合摄动动力系统的鲁棒控制

This Project studies robust stabilities of nonlinear systems described by mixed.perturbations. First, the approach of integral quadratic constraints (IQCs) is generalized to the uncertain systems with both parametric and dynamical perturbations, and the edge and vertex.checking results are obtained for various parametric perturbation modes by using the properties of biconvex and convex-concave functions. Based on this, the stability and perturbation margin of the mixed uncertain systems with controllers are further considered, and the edge and vertex.checking results are obtained for various perturbation modes. Secondly, the robust stability of the nonlinear dynamical systems with feedback uncertainties constrained by norms and class K-functions is also studied, a sufficient criterion for robust stability with less conservativeness.than the small gain theorem is presented. Finally, the problem of the robust controller synthesis for the system with the coprim decomposed perturbations is studied, and the problem of the robust controller synthesis is converted to the problem of solving parameterized linear matrix inequalities by means of convex parameterization and S- procedure.

本项目研究混合摄动动力系统的鲁棒控制。其中参数摄动为凸多面体不确定系统族，非参数摄动为算子图不等式约束下的输入输出算子族。将系统的稳定性及性能表示为参数化的不等式约束，在此条件下研究系统鲁棒稳定性的检验、系统鲁棒性能的检验、系统鲁棒镇定的条件及系统鲁棒稳定的摄动界。最终给出研究混合摄动系统鲁棒控制的统一方法。