Robust stability and stabilization of discrete-time non-linear systems: The LMI approach

D. M. Stipanović, D. D. Šiljak

Research output: Contribution to journalArticlepeer-review


The purpose of this paper is to convert the problem of robust stability of a discrete-time system under non-linear perturbation to a constrained convex optimization problem involving linear matrix inequalities (LMI). The nominal system is linear and time-invariant, while the perturbation is an uncertain non-linear time-varying function which satisfies a quadratic constraint. We show how the proposed LMI framework can be used to select a quadratic Lyapunov function which allows for the least restrictive non-linear constraints. When the nominal system is unstable the framework can be used to design a linear state feedback which stabilizes the system with the same maximal results regarding the class of non-linear perturbations. Of particular interest in this context is our ability to use the LMI formulation for stabilization of interconnected systems composed of linear subsystems with uncertain non-linear and time-varying coupling. By assuming stabilizability of the subsystems we can produce local control laws under decentralized information structure constraints dictated by the subsystems. Again, the stabilizing feedback laws produce a closed-loop system that is maximally robust with respect to the size of the uncertain interconnection terms.

Original languageEnglish (US)
Pages (from-to)873-879
Number of pages7
JournalInternational Journal of Control
Issue number9
StatePublished - Jun 15 2001
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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