Upper Bounds for Induced Operator Norms of Nonlinear Systems

In this paper, new methods are introduced to compute the L ₁, L ₂, and L _infin (lscr ₁, lscr ₂ and lscr _infin) induced operator norms of continuous (discrete) nonlinear systems. These methods are based on the so-called sigmav_A representation of nonlinear systems, which is introduced earlier by the authors. The methods are applicable if a certain condition is satisfied by the parameter of the sigmav_A representation. Two examples are provided to show the applicability of the methods. In addition, another method is suggested to derive an upper bound on the L _infin (lscr _infin) norm of the system output. This method does not suffer from the limitations of the pervious ones.