Stabilizing Controllers for Multi-Input, Singular Control Gain Systems

TL;DR

This paper introduces a new control design methodology for stabilizing multi-input linear systems with time-varying, singular control gains, extending previous results and demonstrating applications in spacecraft stabilization and observer design.

Contribution

It presents a novel persistence filter construction and extends stabilization techniques to multi-input systems with singular, time-varying gains, including observer development.

Findings

Successful stabilization of multi-input systems with singular gains.

Application to spacecraft stabilization demonstrating practical effectiveness.

Development of an observer for systems with singular measurement gains.

Abstract

This paper proposes a new methodology for design of a stabilizing control law for multi-input linear systems with time-varying, singular gains on the control. The results presented here assume the control gain to satisfy persistence of excitation which is a necessary condition for existence of stabilizing controllers in the presence of unstable drift. This work involves a novel persistence filter construction and provides a significant extension to the authors' previous result on stabilization of single-input linear systems with time-varying singular gains. An application to underactuated spacecraft stabilization is shown which illustrates the interesting features of the time-varying control design in stabilization of nonlinear dynamical systems. Finally, the development of an observer counterpart of these results is presented in the presence of multiple-outputs subject to singular measurement gains.