Abstract

Exactly solvable chaos is used to control unstable, high-dimensional linear systems and yield bounded dynamics. Piecewise-constant feedback with periodic switching is derived assuming a system matrix with distinct, real eigenvalues. The controlled system exhibits exactly solvable chaos in each unstable dimension. Examples demonstrate controller efficacy for bounding the unstable dynamics.  Surprisingly, numerical simulations also show effective control in systems with complex conjugate eigenvalues. These results expand exactly solvable chaos to now include high-dimensional hybrid dynamical systems.