The largest divergence rate is a characterization of the stability behavior for dynamic systems, which has been proven to be equal to the least possible common matrix set measure (extreme measure) of switched linear systems. To determine the largest divergence rate is an interesting and open problem. In this paper, an algorithm is introduced to estimate the largest divergence rate for a class of the 3rd-order switched linear systems, by which any desired accurate estimation could be derived. It explores a way to determine the largest divergence rate for the 3rd-order switched linear systems. Furthermore, the accurate estimation provides a qualitative and quantitative analysis for guaranteed stability of switched linear systems.
In this work, we study the robust observer-driven switching stabilization problem of switched linear systems. Under the condition that each subsystem is completely observable, with the observer-driven switching law which makes the system exponentially stable for the nominal system, we prove that the overall system is robust against structural/switching perturbations and is input/output to state stable for unstructural perturbations.
