Analysing the Stability of Linear Systems via Exponential Chebyshev Polynomials

We analyze the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. In case of matrices with real spectrum, we obtain a lower bound for the Euler step size to decide stability. This leads to a method for computing the Lyapunov exponent with a given accuracy and with a guaranteed computational cost. Our approach is based on the analysis of Chebyshev systems of exponents.