Distributed Wireless Networked 𝐻_∞ Control for a Class of Lurie-Type Nonlinear Systems

Algorithm 3

Given a scalar 𝛾>0, solving the 𝐻_∞  fading WNCN with unreliable communication links for closed-loop system 𝒢.

Step  1. Set 𝑘=0. If there exists an initial feasible solution set Υ₀=𝑃,𝑄,𝑅,Σ,𝑊^𝒪_𝜇,𝑊^𝒞_𝜇,𝑊^ℐ_𝜇 satisfying the constraints

   (42)–(44), let 𝒳₀=𝑃, 𝒴₀=𝑄. Otherwise, exit.

Step  2. If 𝑘≤𝜅, go to Step  3 where 𝜅 is the assumed maximum number of iteration. Otherwise, exit.

Step  3. At 𝑘≥0, obtain the feasible solution set Υ_𝑘+1=𝑃,𝑄,𝑅,Σ,𝑊^𝒪_𝜇,𝑊^𝒞_𝜇,𝑊^ℐ_𝜇 by solving the following LMI problem:

    min𝐓𝐫𝒳_𝑘𝑄+𝒴_𝑘𝑃 s.t. (42)–(44).

Step  4. Substitute Υ_𝑘+1 into matrix Ξ₁. If inequality Ξ₁≺0 holds, stop the algorithm. Otherwise, set 𝑘=𝑘+1, 𝒳_𝑘=𝑃,

    𝒴_𝑘=𝑄 and go to Step  2.