# American Institute of Mathematical Sciences

January  2015, 2(1): 65-81. doi: 10.3934/jcd.2015.2.65

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

 1 University of Bayreuth, Chair of Applied Mathematics, Universitätsstraße 30, 95440 Bayreuth 2 University of Bayreuth, Chair of Applied Mathematics, Universitãtsstraße 30, 95440 Bayreuth, Germany

Received  April 2014 Revised  January 2015 Published  August 2015

We present an event-based numerical design method for an input-to-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.
Citation: Lars Grüne, Manuela Sigurani. Numerical event-based ISS controller design via a dynamic game approach. Journal of Computational Dynamics, 2015, 2 (1) : 65-81. doi: 10.3934/jcd.2015.2.65
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