ISS Interval Observers for Nonlinear Switched Systems under Constrained Switching

In this paper, interval observers are synthesized for globally Lipschitz nonlinear switched systems. Interval observers are designed to ensure positivity and input-to state (ISS) stability of the error dynamics. The first result synthesizes interval observers where some of the modes of the nonlinear error dynamics can be destabilizing. ISS is guaranteed if the activation time of the unstable modes is constrained. The second result uses coordinate transformations. Impulses are applied when switching between each modes coordinate frame to preserve positivity. These impulses tend to be destabilizing, so ISS is guaranteed if switching does not occur too frequently.