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On Poly-Quadratic Stabilizability and Detectability of Polytopic LPV Systems

T. J. Meijer, V. S. Dolk, W. P. M. H. Heemels

Abstract

In this technical communique, we generalize the well-known Lyapunov-based stabilizability and detectability tests for discrete-time linear time-invariant systems to polytopic linear parameter-varying systems using the class of so-called poly-quadratic Lyapunov functions.

On Poly-Quadratic Stabilizability and Detectability of Polytopic LPV Systems

Abstract

In this technical communique, we generalize the well-known Lyapunov-based stabilizability and detectability tests for discrete-time linear time-invariant systems to polytopic linear parameter-varying systems using the class of so-called poly-quadratic Lyapunov functions.
Paper Structure (10 sections, 39 equations, 2 figures)

This paper contains 10 sections, 39 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Parameter-sequence-dependent systems
  3. Stability notion
  4. Detectability notion
  5. Stabilizability notion
  6. Main results
  7. Poly-Q-detectability test
  8. Poly-Q stabilizability test
  9. Conclusions
  10. Existing technical lemmas

Figures (2)

  • Figure 1: Overview of poly-Q detectability conditions.
  • Figure 2: Overview of poly-Q stabilizability conditions.

Theorems & Definitions (3)

  • proof
  • proof
  • proof