Remarks on input-to-state stability of collocated systems with saturated feedback

Jacob, Birgit; Schwenninger, Felix L.; Vorberg, Lukas A.

doi:10.1007/s00498-020-00264-w

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…See [33], [7], [34], [35] and, respectively, [40], [21], [36] among many others. And finally, a multitude of papers have recently been published on fundamental characterizations and criteria for input-to-state stability [29], [30], [17], [15], [18], [19] and for versions of input-to-state stability like local [28], integral [15], strong [37], weak [45] and input-to-state practical stability [32], for instance. A nice survey of the state of the art of input-to-state stability for infinite-dimensional systems can be found in [36] -along with an extensive list of references on the topic.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of port-Hamiltonian systems by nonlinear boundary control in the presence of disturbances

Schmid

Zwart

2021

ESAIM: COCV

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In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order $N \in \N$ on a bounded $1$-dimensional spatial domain $(a,b)$. In order to achieve stabilization, we couple the system to a dynamic boundary controller, that is, a controller that acts on the system only via the boundary points $a,b$ of the spatial domain. We use a nonlinear controller in order to capture the nonlinear behavior that realistic actuators often exhibit and, moreover, we allow the output of the controller to be corrupted by actuator disturbances before it is fed back into the system. What we show here is that the resulting nonlinear closed-loop system is input-to-state stable w.r.t.~square-integrable disturbance inputs. In particular, we obtain uniform input-to-state stability for systems of order $N=1$ and a special class of nonlinear controllers, and weak input-to-state stability for systems of arbitrary order $N \in \N$ and a more general class of nonlinear controllers. Also, in both cases, we obtain convergence to $0$ of all solutions as $t \to \infty$. Applications are given to vibrating strings and beams.

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