Controllability of switched differential–algebraic equations

Küsters, Ferdinand; Ruppert, Markus G.-M.; Trenn, Stephan

doi:10.1016/j.sysconle.2015.01.011

Cited by 17 publications

(9 citation statements)

References 17 publications

(25 reference statements)

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“…Another class of systems for which one cannot expect that U (x) = U for all x ∈ X are differential-algebraic equations (DAEs), see e.g. [39], [40].…”

Section: Monotonicity Of Control Systemsmentioning

confidence: 99%

Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances

Mironchenko¹,

Karafyllis²,

Krstić³

2019

SIAM J. Control Optim.

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We introduce a monotonicity-based method for studying input-to-state stability (ISS) of nonlinear parabolic equations with boundary inputs. We first show that a monotone control system is ISS if and only if it is ISS w.r.t. constant inputs. Then we show by means of classical maximum principles that nonlinear parabolic equations with boundary disturbances are monotone control systems.With these two facts, we establish that ISS of the original nonlinear parabolic PDE with constant boundary disturbances is equivalent to ISS of a closely related nonlinear parabolic PDE with constant distributed disturbances and zero boundary condition. The last problem is conceptually much simpler and can be handled by means of various recently developed techniques.

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“…Another class of systems for which one cannot expect that U (x) = U for all x ∈ X are differential-algebraic equations (DAEs), see e.g. [39], [40].…”

Section: Monotonicity Of Control Systemsmentioning

confidence: 99%

Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances

Mironchenko¹,

Karafyllis²,

Krstić³

2019

SIAM J. Control Optim.

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“…Controllability and reachability are analzyed analogous to the work [4]. The results on observability and determinability are based on [8], [10].…”

Section: System Theoretic Propertiesmentioning

confidence: 99%

“…[11,Prop. 7] and [4,Rem. 3.2]) that a switched ODE with jumps is controllable on [0, T ] iff for any initial value x 0 ∈ R n there exists a solution (u, x, y) ∈ B σ with x(0 − ) = x 0 and x(T + ) = 0.…”

Section: A Definitionsmentioning

confidence: 99%

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Duality of switched ODEs with jumps

Küsters

Trenn

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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Duality between controllability/reachability and determinability/observability of switched systems with jumps is proven. The duality result is based on the recent characterization of controllability for switched differential-algebraic equations (DAEs) which share many properties with switched ordinary differential equations (ODEs) with jumps. Here we view the switching signal as given and fixed, which makes the overall switched system time-varying, in particular controllability and reachability do not coincide anymore

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“…Several other structural properties of (switched) DAEs have been studied recently. Among those are controllability [6], stability [7] and observability [8]. However, impulse controllability has thus far only been studied in the nonswitched case [9]- [12] and, to the best of the authors knowledge, there are no results yet for the switched case.…”

Section: Introductionmentioning

confidence: 99%

Impulse controllability of switched differential-algebraic equations

Wijnbergen

Trenn

2020

2020 European Control Conference (ECC)

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This paper addresses impulse controllability of switched DAEs on a finite interval. First we present a forward approach where we define certain subspaces forward in time. These subpsaces are then used to provide a sufficient condition for impulse controllability. In order to obtain a full characterization we present afterwards a backward approach, where a sequence of subspaces is defined backwards in time. With the help of the last element of this backward sequence, we are able to fully characterize impulse controllability. All results are geometric results and thus independent of a coordinate system.

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Controllability of switched differential–algebraic equations

Cited by 17 publications

References 17 publications

Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances

Monotonicity Methods for Input-to-State Stability of Nonlinear Parabolic PDEs with Boundary Disturbances

Duality of switched ODEs with jumps

Impulse controllability of switched differential-algebraic equations

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