Computing upper-bounds of the minimum dwell time of linear switched systems via homogeneous polynomial Lyapunov functions

This paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization problems based on linear matrix inequalities (LMIs). This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based on Kronecker products, and the other on the square matrix representation (SMR). Some examples illustrate the use and the potentialities of the proposed approach. It is also conjectured that the proposed approach is asymptotically nonconservative, i.e. the exact minimum dwell time is obtained by using homogeneous polynomials with sufficiently large degree.