Stability under dwell time constraints: Discretization revisited
Abstract
We decide the stability and compute the Lyapunov exponent of continuous-time linear switching systems with a guaranteed dwell time. The main result asserts that the discretization method with step size~h approximates the Lyapunov exponent with the precision~C\,h2, where~C is a constant. Let us stress that without the dwell time assumption, the approximation rate is known to be linear in~h. Moreover, for every system, the constant~C can be explicitly evaluated. In turn, the discretized system can be treated by computing the Markovian joint spectral radius of a certain system on a graph. This gives the value of the Lyapunov exponent with a high accuracy. The method is efficient for dimensions up to, approximately, ten; for positive systems, the dimensions can be much higher, up to several hundreds.