This paper provides a Lyapunov-based small-gain theorem for input-to-state stability (ISS) of networks composed infinitely many finite-dimensional systems. We model these on infinite-dimensional ? ? -type spaces. A crucial assumption in our results is that the internal Lyapunov gains, modeling influence subsystems each other, are linear functions. Moreover, gain operator built from gains assume...

We consider affine control systems with the finite L2-gain property in the case the storage function is nondifferentiable. We generalize some classical results concerning the connection of the finite L2-gain property with the stability properties of the unforced system, the characterization of finite L2gain by means of partial differential inequalities of the Hamilton-Jacobi type and the proble...