The quadratic matrix inequality in singular $H_\infty$ control with state feedback

A.A. Stoorvogel, H.L. Trentelman

    Research output: Contribution to journalArticleAcademicpeer-review

    35 Citations (Scopus)
    112 Downloads (Pure)

    Abstract

    In this paper the standard $H_\infty $ control problem using state feedback is considered. Given a linear, time-invariant, finite-dimensional system, this problem consists of finding a static state feedback such that the resulting closed-loop transfer matrix has $H_\infty $ norm smaller than some a priori given upper bound. In addition it is required that the closed-loop system is internally stable. Conditions for the existence of a suitable state feedback are formulated in terms of a quadratic matrix inequality, reminiscent of the dissipation inequality of singular linear quadratic optimal control. Where the direct feedthrough matrix of the control input is injective, the results presented here specialize to known results in terms of solvability of a certain indefinite algebraic Riccati equation.
    Original languageEnglish
    Pages (from-to)1190-1208
    Number of pages19
    JournalSIAM Journal on Control and Optimization
    Volume28
    Issue number5
    DOIs
    Publication statusPublished - 1990

    Fingerprint

    Dive into the research topics of 'The quadratic matrix inequality in singular $H_\infty$ control with state feedback'. Together they form a unique fingerprint.

    Cite this