Stabilization for a semilinear heat equation with switching control

Wen Kang, Emilia Fridman, Chuan Xin Liu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This work discusses sampled-data stabilization by switching for 1-D nonlinear reaction-diffusion equation with spatially scheduled actuators. We suggest that the interval [0,1] is divided into N subdomains. We assume that N sensors are placed in each subdomain and measure the average value of the state in the discrete time. We stabilize the system by switching sampled-data static output-feedback. This switching control law can be implemented either by using one moving actuator that can move to the active subdomain in the negligible time or by N actuators placed in each subdomain. In the latter case switching control may reduce the energy that the system spends. Constructive conditions are derived to ensure that the resulting closed-loop system is exponentially stable by means of the Lyapunov approach. A numerical example shows the efficiency of the method.

Original languageEnglish
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665436595
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: 13 Dec 202117 Dec 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control


Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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