# Consensus of fractional-order multi-agent systems: Matrix inequality approach

## TL;DR

This paper presents a systematic LMI-based method for robust stabilization of fractional-order nonlinear multi-agent systems using fixed-order dynamic output feedback controllers, avoiding iterative searches and constraints on state matrices.

## Contribution

Introduces a direct Lyapunov-based LMI approach for designing low-order output feedback controllers for fractional-order systems without iterative or restrictive conditions.

## Key findings

- Effective stabilization demonstrated through simulations
- No constraints on state space matrices
- Straightforward design procedure

## Abstract

This paper investigates the robust stabilisation of a class of fractional-order non-linear systems via fixed-order dynamic output feedback controller in terms of linear matrix inequalities (LMIs). The systematic stabilisation algorithm design for low-order controller based on direct Lyapunov approach is proposed. In the presented algorithm the conditions containing the bilinear variables are decoupled into separate conditions without imposing equality constraints or considering an iterative search of the controller parameters. There is no any limiting constraint on the state space matrices and also we assumed the most complete output feedback controller. Simulations results are given to approve the effectiveness and the straightforwardness of the proposed design.

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Source: https://tomesphere.com/paper/1906.02139