Average Consensus Analysis of Distributed Inference with Uncertain Markovian Transition Probability

Algorithm 1

Choose TOL>0;

Choose enough large 𝜌₁∈ℝ such that Ξ(𝛼,𝜌₁) has solutions;

Choose enough small 𝜌₂∈ℝ such that Ξ(𝛼,𝜌₂) has no solution;

repeat until 𝜌₁−𝜌₂<TOL

   𝜌₀←(𝜌₁+𝜌₂)/2;

  Solve Ξ(𝛼,𝜌₀)<0

   if  Ξ(𝛼,𝜌₀)<0 has solutions

   𝜌₁←𝜌₀;

   else

   𝜌₂←𝜌₀;

end (repeat)

Set  𝜌(𝛼)←𝜌₁.