POLE MOBILITY AND MINIMAL NORM STABILIZATION OF SISO SYSTEMS UNDER BOUNDED STATE-FEEDBACK

This paper examines the fundamental system properties of pole mobility and stabilizability under bounded feedback for the case of single-inp ut single-output (SISO) systems, where the constraints on the feedback are defined in terms of the L2 norm. It is shown that the bounded gai n assumption implies a bounded norm condition on the coefficient vecto r associated with the closed-loop characteristic polynomial. Classical and new results on the root distribution of bounded coefficient polyn omials are reviewed first. With these results, the closed-loop pole mo bility of SISO systems under bounded state feedback is studied. It is shown that the assignable closed-loop poles are always within bounded regions, and alternative estimates for these regions are given. Exact boundaries are also established by utilizing computational methods. A common computational scheme is also developed to calculate the distanc es of stable polynomials from instability and the distance of unstable polynomials from stability. Finally, for open loop unstable systems, the problems of stabilization and delta-stabilization under the L2 nor m restriction are considered. The minimal norm required for stabilizin g or delta-stabilizing unstable systems can be found.