Small-gain theorem, gain assignment and applications

We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag (1989). It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions of the components is smaller than the identity function. The second one shows an example of gain function assignment by feedback. Applications to the problem of global stabilization via partial-state feedback and output feedback are also considered