Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems

Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)


In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is "exact" in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.

Original languageEnglish
Pages (from-to)14-25
Number of pages12
Issue number1
Publication statusPublished - Jan 1 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


Dive into the research topics of 'Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems'. Together they form a unique fingerprint.

Cite this