2024/02/07 by Thomas Mejstrik, Vladimir Yu. Protasov, Mejstrik, Thomas +1
Engineering · Mathematics · #15A60 #37C20 #49M25 #93C30 #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2402.04795
openalex publication_date 2024/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.