<i>L</i>₂ Gain for Ultimately Bounded Systems With Application to Quantized Input Systems

This paper discusses the gain of nonlinear systems which, in the absence of exogenous inputs, are uniformly ultimately bounded. Unlike for many systems which are asymptotically stable in the absence of exogenous inputs, it is not possible to infer standard gain conditions for systems which are only known to be ultimately bounded. This paper gives another interpretation of gain and shows that, under some assumptions, consideration of a typical performance objective leads to satisfaction of this new interpretation of gain -called the gain. This is harnessed for performance analysis of systems with quantized inputs and an approach to computing the gain is presented.