Stabilizing Controllers for Multi-Input, Singular Control Gain Systems
For control theorists and engineers dealing with underactuated systems, this work provides a method to stabilize systems where control gains can vanish, but it is an incremental extension of prior single-input results.
This paper extends a previous single-input stabilization method to multi-input linear systems with time-varying singular control gains, using a novel persistence filter. It demonstrates the approach on underactuated spacecraft stabilization and develops an observer counterpart for multiple-output systems with singular measurement gains.
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.