Time Domain Control Design for Robust Stability of Linear Regulators: Application to Aircraft Control

This paper addresses the aspect of `Stability Robustness´ of linear systems in time domain. Upper bounds on the linear perturbation of an asymptotically stable linear system are obtained to maintain stability, both for `structured´ as well as `unstructured´ perturbations using Liapunov approach. A quantitative measure called `Stability Robustness Index´ is introduced and this measure is used to design `robust´ controllers for Linear Quadratic (LQ) Regulators. The proposed control design algorithm can be used, for given set of perturbations, to select the range of control effort for which the system is stability robust. Conversely it can also be used, for given control effort, to determine the range of the size of allowable perturbations. The algorithm is illustrated with the help of an aircraft control example. The scope of the proposed research and its extension to LQG Regulators, dynamic compensator design and other applications are discussed.