Comments on L2-gain Analysis of Systems with Persistent Outputs

In this paper, a generalization of the L2-gain inequality utilizing \point to set" distances [11, 10] is applied to cope with systems with persistent excitation. This generalization is compared with notions of power gain introduced in [4]. In particular it is found that the gain inequality associated with \point to set" distances freely admits a de nition of available storage and allows the standard Hamilton-Jacobi-Bellman PDE to be generalized in a simple way. Issues concerning stability are also addressed. The nature of the generalized L2-gain inequality admits a simple understanding of stability, which is an improvement over the power gain generalization. However, casting optimal control problems is less satisfying in that it is more diÆcult to minimize the power generated by the system.