Upper Bounds on Peaks in Discrete-Time Linear Systems

U. M. Ahiyevich, S. E. Parsegov, P. S. Shcherbakov

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Trajectories of stable linear systems with nonzero initial conditions are known to deviate considerably from the zero equilibrium point at finite time instances. In the paper we analyze transients in discrete-time linear systems and provide upper bounds on deviations (peaks) via use of linear matrix inequalities. An approach to peak-minimizing feedback design is also proposed. An analysis of peak effects for norms of powers of Schur stable matrices is presented and a robust version of the problem is considered. The theory is illustrated by numerical examples.

Original languageEnglish
Pages (from-to)1976-1988
Number of pages13
JournalAutomation and Remote Control
Issue number11
Publication statusPublished - 1 Nov 2018


  • linear discrete-time systems
  • linear matrix inequalities
  • nonzero initial conditions
  • robustness
  • stability
  • transient behavior
  • upper bounds


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