Constrained output feedbacks for singularly perturbed imperfectly known nonlinear systems

Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey

“…where Ax and EA z are the costates or adjoints corresponding to the states x(t) andz(t), respectively, and H is the Hamiltonian given by (41)…”

Stabilizing Feedback Controls for a Class of Singularly Perturbed, Nonlinear, Uncertain, Time-Delay Systems

“…In this final stage it is shown that, using the memoryless feedback (8), the full-order uncertain system (1-2) is globally uniformly ultimately bounded with respect to some compact set. The methodology follows that of (Corless and Ryan, 1991) (see, also, (Binning and Goodall, 1999)) in which a Lyapunov analysis is used for delay-free systems. Consider the functional defined by…”

“…This particular problem can be addressed utilizing singular perturbation theory (for more details, see (Kokotovic et al, 1986) or, for a differentialgeometric approach, (Isidori, 1989)). There has been much research, over the past decades, on control of uncertain singularly perturbed systems using a deterministic approach; for example, (Binning and Goodall, 1999;Binning and Goodall, 2000;Corless, 1991;Corless et al, 1993;Corless et al, 1990;Corless and Ryan, 1991;Garofalo and Leitmann, 1990), and (Leitmann et al, 1986), to name but a few. In addition, time-delays, which can have a significant effect on the dynamic behaviour of a system, is a phenomenon that has been investigated by a number of researchers in recent times; in particular, aspects of stability analysis using a deterministic approach.…”

“…One component of a controller assures desired behaviour of the slow dynamics, whilst a second component yields the desired stability properties for the fast dynamics in the presence of the active slow controller. The stability analysis is similar to that used in (Binning and Goodall, 1999) and (Binning and Goodall, 2000) but, here, the full-order system is a nonlinear delay system of the retarded-type, containing both discrete and distributed delays. Utilizing memoryless feedback controllers, together with a deterministic methodology based on Lyapunov theory and Lyapunov-Krasovskiȋ functionals, some stability criteria are proposed that will ensure the desired stability property for the prescribed class of singularly perturbed delay systems, provided the singular perturbation parameter is small enough.…”

“…The design of the feedback controls emulates the work in (Corless, 1991) and (Binning and Goodall, 1999).…”