Topological entropy control via static feedback synthesis for continuous-time linear time-invariant systems

The topological entropy is a measure that quantifies the unstable of a dynamical system, and plays a key role in feedback stabilization. This paper addresses the problem of designing static feedback controllers for reducing the topological entropy in continuous-time linear time-invariant systems. It is shown that a sufficient condition for determining a controller (if any) that reduces the topological entropy under a desired upper bound can be obtained by solving a convex optimization problem, in particular a semidefinite program (SDP). Moreover, it is shown that this condition is also necessary by sufficiently increasing the size of the SDP. Some numerical examples illustrate the proposed methodology.