Numerical methods for linear time-invariant systems analysis and design in the behavioral setting

Analysis and design of dynamical systems is transitioning from a model-based to a data-driven paradigm. Theoretical foundation for the data-driven paradigm is provided by the behavioral approach, which views systems as sets of trajectories, however, currently it lacks robust and efficient computational methods. A key sub problem is computing a basis for the finite-horizon behavior. This can be done using a parametric representation or trajectories of the system. The obtained basis for the finite-horizon behavior is a non-parametric representation of the system. Contrary to classical non-parametric representations, e.g., impulse response and frequency response, it is finite and exact, captures nonzero initial conditions, and is applicable to uncontrollable systems. It also leads to new computational methods for systems analysis, signal processing, and control. Examples presented in the paper are finding the system’s complexity, finding an input/output partitioning of the variables, and checking controllability.