SYSTEM ORDER REDUCTION IN ROBUST STABILIZATION PROBLEMS

Robust stabilization via state-feedback is considered. Using a fixed q uadratic Lyapunov function approach (quadratic stabilization) we inves tigate the possibility of reducing the quadratic stabilization problem of a given uncertain system to a similar problem for an uncertain sub system with a fewer number of states, this subsystem is the so-called regular subsystem associated with the original system. It is shown tha t when some of the control input channels of the given uncertain syste m are 'free of uncertainty', this reduction is possible. We show that a given uncertain system is quadratically stabilizable via linear stat e-feedback if and only if the same holds for its regular subsystem. Wh en the regular subsystem is quadratically stabilizable via linear stat e-feedback, a simple formula for a controller that quadratically stabi lizes the original system is given. We also present an example of an u ncertain system that is not quadratically stabilizable even though its regular subsystem can be quadratically stabilized via nonlinear state -feedback. Thus, the above equivalence between the original system and its regular subsystem from the point of view of quadratic stabilizabi lity breaks down if nonlinear controllers are considered.