Comments on ℒ2-gain analysis of systems with persistent outputs

A generalization of the L₂-gain inequality utilizing “point to set” distances is applied to cope with systems with persistent excitation. This generalization is compared with notions of power gain introduced in Dower and James (1998). In particular it is found that the gain inequality associated with “point to set” distances freely admits a definition 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 difficult to minimize the power generated by the system