### Uittreksel

Taal | Engels |
---|---|

Pagina's | 453-458 |

Tijdschrift | IEEE Control Systems Letters |

Volume | 2 |

Nummer van het tijdschrift | 3 |

DOI's | |

Status | Gepubliceerd - 3 jul 2018 |

### Vingerafdruk

### Trefwoorden

- math.OC
- cs.GT
- cs.SY

### Citeer dit

*IEEE Control Systems Letters*,

*2*(3), 453-458. DOI: 10.1109/LCSYS.2018.2840882

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*IEEE Control Systems Letters*, vol. 2, nr. 3, blz. 453-458. DOI: 10.1109/LCSYS.2018.2840882

**On the convergence of discrete-time linear systems : A linear time-varying Mann iteration converges iff the operator is strictly pseudocontractive.** / Belgioioso, Giuseppe; Fabiani, Filippo; Blanchini, Franco; Grammatico, Sergio.

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

TY - JOUR

T1 - On the convergence of discrete-time linear systems

T2 - IEEE Control Systems Letters

AU - Belgioioso,Giuseppe

AU - Fabiani,Filippo

AU - Blanchini,Franco

AU - Grammatico,Sergio

PY - 2018/7/3

Y1 - 2018/7/3

N2 - We adopt an operator-theoretic perspective to study convergence of linear fixed-point iterations and discrete- time linear systems. We mainly focus on the so-called Krasnoselskij-Mann iteration x(k+1) = ( 1 - \alpha(k) ) x(k) + \alpha(k) A x(k), which is relevant for distributed computation in optimization and game theory, when A is not available in a centralized way. We show that convergence to a vector in the kernel of (I-A) is equivalent to strict pseudocontractiveness of the linear operator x -> Ax. We also characterize some relevant operator-theoretic properties of linear operators via eigenvalue location and linear matrix inequalities. We apply the convergence conditions to multi-agent linear systems with vanishing step sizes, in particular, to linear consensus dynamics and equilibrium seeking in monotone linear-quadratic games.

AB - We adopt an operator-theoretic perspective to study convergence of linear fixed-point iterations and discrete- time linear systems. We mainly focus on the so-called Krasnoselskij-Mann iteration x(k+1) = ( 1 - \alpha(k) ) x(k) + \alpha(k) A x(k), which is relevant for distributed computation in optimization and game theory, when A is not available in a centralized way. We show that convergence to a vector in the kernel of (I-A) is equivalent to strict pseudocontractiveness of the linear operator x -> Ax. We also characterize some relevant operator-theoretic properties of linear operators via eigenvalue location and linear matrix inequalities. We apply the convergence conditions to multi-agent linear systems with vanishing step sizes, in particular, to linear consensus dynamics and equilibrium seeking in monotone linear-quadratic games.

KW - math.OC

KW - cs.GT

KW - cs.SY

U2 - 10.1109/LCSYS.2018.2840882

DO - 10.1109/LCSYS.2018.2840882

M3 - Article

VL - 2

SP - 453

EP - 458

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 3

ER -