Stability results for switched controller systems
The paper considers a stability problem for the switched linear system \[ \dot x=Ax+Bu(t) \] \[ u=L_{i_k}x,\;i_k\in I(x) \] where \(I(\cdot)\) is a set of indices that is state dependent. The main feature of the paper is to consider stability properties on the switching boundaries by employing Filippov solutions. This is a crucial step for robust stability. Necessary and sufficient conditions for quadratic stabilization are given.
scientific article; zbMATH DE number 1331859