Optimal persistent disturbance attenuation control for linear hybrid systems

Hai Lin, Guisheng Zhai, Panos J. Antsaklis

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


In this paper, the disturbance attenuation properties for a class of linear hybrid systems are investigated, and a hybrid optimal persistent disturbance attenuation control problem is studied. First, a procedure is developed to determine the minimal l induced gain of linear hybrid systems. However, for general hybrid systems, the termination of the procedure is not guaranteed. Then, the decidability issues are discussed. The termination of the procedure in a finite number of steps is shown for a subclass of hybrid systems with simplified discrete event dynamics, called switched linear systems. Finally, the optimal persistent disturbance attenuation controller synthesis problem is studied. It is shown that the optimal performance level can be achieved by a piecewise linear state feedback control law, and a systematic approach is proposed to design such feedback control.

Original languageEnglish
Pages (from-to)1231-1250
Number of pages20
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number6
Publication statusPublished - 2006 Sept 15
Externally publishedYes


  • Disturbance attenuation
  • Hybrid dynamical systems
  • Induced gain
  • Invariant sets
  • Robust performance
  • Switched systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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