Subspace attractivity and invariance: Ultimate attainment of prescribed dynamic behaviour

Abstract

The outline of the chapter is as follows. We begin with a brief resume of relevant concepts and results from the theory of differential inclusions. The class of uncertain systems to be considered in then made precise. We continue with a treatment of the variable structure systems concept of an invariant subspace ℒ (with prescribed dynamic behaviour therein) and construct a discontinuous feedback strategy which renders if globally finite-time attractive (thereby ensuring ultimate attainment of prescribed dynamic behaviour). The approach is essentially that of Ryan & Corless (1984) (with origins in Corless & Leitmann, 1981), subsequently recast in a differential inclusion setting by Goodall & Ryan (1986, 1988). Finally, our results are extended to problems of tracking and model following.