STRUCTURED DISSIPATIVENESS AND ABSOLUTE STABILITY OF NONLINEAR-SYSTEMS

The paper considers a problem of absolute stability for a nonlinear un certain system with structured uncertainty. An S-procedure for nonline ar systems is established and, using this, the paper shows that the ab solute stability problem is equivalent to an absolute stability proble m for a nonlinear uncertain system with unstructured uncertainty. The paper also introduces a new notion of structured dissipativeness for n onlinear systems. This notion extends the standard notion of dissipati veness in that it allows for multiple supply functions. The paper show s that a nonlinear uncertain system containing structured uncertaintie s will be absolutely stable if and only if a corresponding structured dissipativeness condition is satisfied. It is also shown that structur ed dissipativeness is equivalent to the standard notion of dissipative ness with a parameter dependent supply function.