SMALL-GAIN THEOREM FOR ISS SYSTEMS AND APPLICATIONS

We introduce a concept of input-to-output practical stability (IOpS) w hich is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is aga in an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the in terest of these results, we address the problem of global asymptotic s tabilization via partial-state feedback for linear systems with nonlin ear, stable dynamic perturbations and for systems which have a particu lar disturbed recurrent structure.