Computing Upper-bounds of the Minimum Dwell Time of Linear\ud Switched Systems via Homogeneous Polynomial Lyapunov Functions

摘要

This paper investigates the minimum dwell time\udfor switched linear systems. It is shown that a sequence of\udupper bounds of the minimum dwell time can be computed\udby exploiting homogeneous polynomial Lyapunov functions\udand convex optimization problems based on linear matrix\udinequalities (LMIs). This sequence is obtained by adopting\udtwo possible representations of homogeneous polynomials, one\udbased on Kronecker products, and the other on the square\udmatrix representation (SMR). Some examples illustrate the\uduse and the potentialities of the proposed approach. It is also\udconjectured that the proposed approach is asymptotically nonconservative,\udi.e. the exact minimum dwell time is obtained by\udusing homogeneous polynomials with sufficiently large degree.