Stability analysis of switching TS models using α-samples approach

In this paper we consider stability analysis of discrete-time switching systems represented by Takagi-Sugeno fuzzy models. For the analysis we use a switching Lyapunov function defined on the switches. In order to develop stability conditions, we consider the variation of this function along switching paths of length α, i.e., an α sample variation of the Lyapunov function. This approach is able to determine stability of a switching system containing unstable local models. The developed conditions can be formulated as LMIs and they are illustrated on a numerical example.