A novel approach to stability analysis for switched positive linear systems

This paper is concerned with exploring less conservative stability conditions for a class of switched positive linear systems. A switched matrix-parameterized copositive Lyapunov function (SMPCLF) is first introduced, where “matrix-parameterized” implies that the parameters of the constructed Lyapunov function are distributed in a matrix, which is different from the traditional vector-parameterized copositive Lyapunov function. Based on the proposed SMPCLF, a new stability criterion is derived for the underlying systems under arbitrary switching. Furthermore, by performing higher order relaxations in the SMPCLF and its time difference by positive states, the conservativeness can be further reduced. A numerical example is given to demonstrate the effectiveness and advantages of the obtained theoretical results.