Hybrid dynamical systems with controlled discrete transitions

$H_{\infty}$ Bumpless Transfer Under Controller Uncertainty

“…1. This result has been generalized in Ryan [10] for L p inputs, using the same assumption on the global asymptotic stability of the origin and assuming that f from (2) is such that f(1; 0) is locally Lipschitz and for every compact set K 2 n there exists c > 0 such that kf(x; u) 0 f(x; 0)k ckuk 8u 2 m ;x 2 K: (3) It is shown in [10] that if for a u 2 L p ( + ) and an initial state x(0), there exists a state trajectory x defined for all t 0 and x is bounded, then x(t) ! 0 as t !…”

“…For a special class of systems, namely, strictly output passive and zero-state detectable systems (the precise definitions will be given in Section II), we derive a result related to those in [10] and [13]. In Section III, we use a technique from infinite-dimensional linear system theory to show that for any L 2 input there exists a unique state trajectory x defined for all t 0 and x(t) !…”

“…In the online operating context, the steady-state bumpless transfer under controller uncertainty represents a particular hybrid system event-a so-called controlled discrete transition [10]. Indeed, as seen, for example, in Fig.…”