Vibrational feedback control.

In this dissertation, the idea of vibrational feedback control is introduced and a number of applications to various control-theoretic problems are discussed. It is shown that vibrational feedback controllers have additional capabilities in comparison with the time-invariant ones. Specifically, in addition to the assignability of the closed loop poles, vibrational feedback controllers lead to assignability of the zeros. As a result, for any controllable and observable plant there exists a continuous time periodic controller that places both the closed loop poles and all finite control loop zeros at any desired position. The superior performance characteristics of vibrational feedback controllers are utilized in a number of control problems. Vibrational feedback controllers ensure stability of the closed loop system with an infinite gain margin; they can guarantee strong and simultaneous stabilization; they can remove decentralized fixed modes; and they can provide an infinite sector of robust stability for a certain class of nonlinear systems. All of these problems are analyzed in detail in this dissertation.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105193/1/9023585.pdfDescription of 9023585.pdf : Restricted to UM users only