Non-exponential stabilization of linear time-invariant systems by linear time-varying controllers

This paper proposes non-exponential stabilization of linear time-invariant systems by linear time-varying controllers. We consider state feedback and dynamic output feedback to make the states of the closed-loop systems decay non-exponentially.We first introduce a non-exponential stability concept that the state of a zero-input time-varying system converges to the origin with an upper bound provided by a specified function. Then, we give non-exponential stabilizability conditions and time-varying controllers to achieve the behavior defined by a desired upper bound function for the closed-loop system. By the proposed methods, we can realize various non-exponential behaviors, which may improve control performance.