Consensus of Multiagent Systems with Packet Losses and Communication Delays Using a Novel Control Protocol

Table 1

Continuous time and discrete time presentations of agent dynamics.

Agent type	Continuous time system	Discrete time presentation
Single integrator	𝑥̇𝑖(𝑡)=𝑢𝑖(𝑡)	𝑥𝑖𝑡𝑘+1=𝑥𝑖𝑡𝑘+𝑇𝐾∑𝑗∈𝑁𝑖𝑎𝑖𝑗𝑥𝑗𝑡𝑘−𝑥𝑖𝑡𝑘
Double integrator	𝑥̇𝑖(𝑡)=𝑣𝑖𝑣̇(𝑡)𝑖(𝑡)=𝑢𝑖(𝑡)	𝑥𝑖𝑡𝑘+1=𝑥𝑖𝑡𝑘+𝑇𝑣𝑖𝑡𝑘+𝑇^22𝐾∑𝑗∈𝑁𝑖𝑎𝑖𝑗𝑥𝑗𝑡𝑘−𝑥𝑖𝑡𝑘𝑣𝑖𝑡𝑘+1=𝑣𝑖𝑡𝑘+𝑇𝐾∑𝑗∈𝑁𝑖𝑎𝑖𝑗𝑥𝑗𝑡𝑘−𝑥𝑖𝑡𝑘
High-order integrator	𝑥̇𝑖(𝑡)=𝐴𝑥𝑖(𝑡)+𝐵𝑢𝑖(𝑡)	𝑥𝑖𝑡𝑘+1=𝑒^𝐴𝑇𝑥𝑖𝑡𝑘+∫^𝑇0𝑒^𝐴𝑡𝐵𝐾∑𝑗∈𝑁𝑖𝑎𝑖𝑗𝑥𝑗𝑡𝑘−𝑥𝑖𝑡𝑘𝑑𝑡