Reachability Analysis of Linear Dynamic Systems with Constant, Arbitrary, and Lipschitz-Continuous Inputs

This paper sets forth a method for reachability analysis of linear dynamic systems in continuous time that can be used to compute time-domain bounds of states and outputs with floating-point precision. The focus is on the particular initial conditions and inputs that cause state or output trajectories to attain their extreme values in time. Inputs can be constant, arbitrary, or Lipschitz continuous waveforms. Uncertainties in initial conditions and inputs are modeled using zonotopes. The calculations exploit the definition of zonotopes and the modal information of the linear system dynamics.