ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems

Grüne, Lars; Kellett, Christopher M.

doi:10.1109/tac.2014.2321667

Cited by 45 publications

(33 citation statements)

References 24 publications

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“…Since an eventbased closed loop system is inevitably discontinuous, the classical implication-form ISS Lyapunov function from [18] is not an appropriate concept, cf. [13]. Therefore, we use the strong implication-form ISS-Lyapunov function recently introduced in [13], here adapted to the ISpS property.…”

Section: Isps Controller Designmentioning

confidence: 99%

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Numerical event-based ISS controller design via a dynamic game approach

Grüne¹,

Sigurani²

2015

Journal of Computational Dynamics

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Abstract. We present an event-based numerical design method for an inputto-state practically stabilizing (ISpS) state feedback controller for perturbed nonlinear discrete time systems. The controllers are designed to be constant on quantization regions which are not assumed to be small. A transition of the state from one quantization region to another triggers an event upon which the control value changes.The controller construction relies on the conversion of the ISpS design problem into a robust controller design problem which is solved by a set oriented discretization technique followed by the solution of a dynamic game on a hypergraph. We present and analyze this approach with a particular focus on keeping track of the quantitative dependence of the resulting gain and the size of the exceptional region for practical stability from the design parameters of our event-based controller.

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Section: Isps Controller Designmentioning

confidence: 99%

“…[13]. Therefore, we use the strong implication-form ISS-Lyapunov function recently introduced in [13], here adapted to the ISpS property. Definition 4.1.…”

Section: Isps Controller Designmentioning

confidence: 99%

Numerical event-based ISS controller design via a dynamic game approach

Grüne¹,

Sigurani²

2015

Journal of Computational Dynamics

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“…To this end, we first define the event-based cost function on the quantization by (11) and note that Assumption 2 implies g P (x, u) ≥ α( x ). We then define the quantized optimal value function by…”

Section: Game Theoretic Stabilizing Controller Design For Perturmentioning

confidence: 99%

“…Since an event-based closed loop system is inevitably discontinuous, the classical implication-form ISS Lyapunov function from [15] is not an appropriate concept, cf. [11]. Therefore, we use the strong implication-form ISS-Lyapunov function recently introduced in [11], here adapted to the ISpS property.…”

Section: Isps Controller Designmentioning

confidence: 99%

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Construction of event-based ISS controllers on coarse quantizations

Grüne

Sigurani

2014

53rd IEEE Conference on Decision and Control

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Abstract-We consider the construction of event-based inputto-state stabilizing state feedback controllers for perturbed nonlinear discrete time systems. The controllers are designed to be constant on possibly coarse quantization regions. An event is triggered upon every transition of the state from one quantization region to another. The practical contribution of the paper is an algorithmic design approach based on game theoretic ideas, feasible for low dimensional systems. The theoretical contribution consists of a novel piecewise constant event-based ISS Lyapunov function concept which is consistent with the imposed quantization.

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An ISS characterization for discontinuous discrete‐time systems

Geiselhart

Noroozi

2019

Proc Appl Math and Mech

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Input‐to‐state stability (ISS) is an important concept to study robustness properties of nonlinear control systems. The ISS property can be, in particular, characterized by ISS Lyapunov functions. For discrete‐time nonlinear control systems two different forms of ISS Lyapunov functions (implication‐form and dissipation‐form) are known to be equivalent if the dynamics are continuous. However, for discontinuous dynamics the equivalence is no longer satisfied. In this work, we discuss this phenomenon and, eventually, give a complete characterization of ISS in terms of ISS Lyapunov functions.

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ISS-Lyapunov Functions for Discontinuous Discrete-Time Systems

Cited by 45 publications

References 24 publications

Numerical event-based ISS controller design via a dynamic game approach

Numerical event-based ISS controller design via a dynamic game approach

Construction of event-based ISS controllers on coarse quantizations

An ISS characterization for discontinuous discrete‐time systems

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