Robust stabilization of families of linear time-varying plants with applications to singularly perturbed systems

The robust stabilization of families of linear time-varying plants is studied. The concept of graph topology for linear time-invariant plants is generalized to the setting of finite-dimensional linear time-varying plants that are internally stabilizable by output feedback. The authors consider feedback connections of linear time-varying plants and general nonlinear time-varying controllers and show that the graph topology is the weakest topology in which feedback stability is a robust property. Using this result, they derive necessary and sufficient conditions for robust stabilization of parametrized families of linear time-varying plants. Within this framework, the authors state sufficient conditions for robust stabilizability of linear time-varying singularly perturbed systems using general nonlinear time-varying controllers. These are natural extensions of the corresponding sufficient conditions in the linear time-invariant case