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Controllability of discrete-time linear systems on lie groups with finite semisimple center

Thiago Cavalheiro, Alexandre Santana, João Cossich

Abstract

In this paper we stated a condition for the controllability of discrete-time linear systems for the case when the Lie group has finite semisimple center and provided a example in the Lie group $SL_2(\mathbb{R})$.

Controllability of discrete-time linear systems on lie groups with finite semisimple center

Abstract

In this paper we stated a condition for the controllability of discrete-time linear systems for the case when the Lie group has finite semisimple center and provided a example in the Lie group .
Paper Structure (5 sections, 14 theorems, 70 equations)

This paper contains 5 sections, 14 theorems, 70 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. General properties
  4. Conditions for controllability
  5. Semigroups and Controllability

Key Result

Proposition 5

Consider a discrete-time linear control system $x_{k+1} = f(u_k,x_k)$, $u_k \in U$ defined on a Lie group $G$. Then it follows for all $g \in G$ and $u = (u_i)_{i \in \mathbb{Z}} \in \mathcal{U}$ that

Theorems & Definitions (24)

  • Remark 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Proposition 5
  • Lemma 6
  • Proposition 7
  • Lemma 8
  • Proposition 9
  • Remark 10
  • ...and 14 more