4 research outputs found
Remarks on input-to-state stability of collocated systems with saturated feedback
We investigate input-to-state stability (ISS) of infinite-dimensional
collocated control systems subject to saturated feedback. Here, the unsaturated
closed loop is dissipative and uniformly globally asymptotically stable. Under
an additional assumption on the linear system, we show ISS for the saturated
one. We discuss the sharpness of the conditions in light of existing results in
the literature.Comment: 12 page
Local stabilization of an unstable parabolic equation via saturated controls
We derive a saturated feedback control, which locally stabilizes a linear
reaction-diffusion equation. In contrast to most other works on this topic, we
do not assume the Lyapunov stability of the uncontrolled system and consider
general unstable systems. Using Lyapunov methods, we provide estimates for the
region of attraction for the closed-loop system, given in terms of linear and
bilinear matrix inequalities. We show that our results can be used with
distributed as well as scalar boundary control, and with different types of
saturations. The efficiency of the proposed method is demonstrated by means of
numerical simulations
Stability results for infinite-dimensional linear control systems subject to saturations
International audienceThis article deals with the stability analysis and the derivation of ISS-Lyapunov functions for infinitedimensional linear systems subject to saturations. Two cases are considered: 1) the saturation acts in the same space as the control space; 2) the saturation acts in another space, especially a Banach space. For the first case, an explicit ISS-Lyapunov function can be derived. For the second case, we prove the global asymptotic stability of the origin when considering all weak solutions