Optimal Finite-Time State Estimation for Discrete-Time Switched Systems under Switching Frequency Constraint

Algorithm 2

Optimal ℋ_∞ finite-time observer design with minimal bound 𝜀_min.

Step  1. Initialize 𝜂=1, set a variation value Δ𝜂>0 and termination value 𝛾.

Step  2. Setting 𝜂=𝜂+Δ𝜂, solve optimization problem (44) with fixed 𝜂.

Step  3. When the optimization problem (44) is solvable for the first time, the value of 𝜂 recorded as 𝜂_min.

    Then, if 𝜂≥𝜂_min+𝜂, terminate the procedure, otherwise record parameters (𝜂,𝜀_min) pair-wisely

    and go back to Step  2.

Step  4. Select the 𝜂 with smallest 𝜀_min recorded in Step  3. Obtain the locally optimized observer gains and

    ascertain the local optimal value of 𝜀_min=𝜅^{1+𝑓𝑛𝒯𝑛}𝜂^𝒯𝑛𝛿²+𝜅^{𝑓𝑛𝒯𝑛}𝛾²𝑑² near 𝜂 by an unconstrained

    nonlinear optimization approach.