Further results on delay-dependent state feedback $$H_\infty $$ control of linear parameter varying time-delay systems

A numerical method for ℋ2$$ {\mathscr{H}}_2 $$ control of linear delay systems

“…Let the step-size h = 0.01 and choose T = 50, Algorithm 2 yields stabilizing initial values of ⃗ K as The results indicate that, for this example, the LMI approaches 10,12 are unable to seek the stabilizing gain matrices while the proposed method can provide a feasible solution. One reason for this difference is that the sufficient and necessary stability condition (7) for the delay system is used in the proposed method.…”

“…In the following examples, we compare the proposed method with other methods mentioned in the literature. We first use Example 3 to demonstrate the comparison with the LMI‐based $$$ {\mathscr{H}}_{\infty } $$$ control method in References 10 and 12. Then we use Example 4 to demonstrate the comparison with the optimization‐based $$$ {\mathscr{H}}_2 $$$ control method in Reference 18.…”

“…$$ For this case, the uncontrolled system has two unstable characteristic roots and the system is unstable. For comparison, we first use the LMI approaches of References 10 and 12 to solve this example. We only consider the feasible problem for the stabilizing gain matrices.…”

“…For linear systems with time delays, the problem of constructing a stable controller for suppressing exogenous disturbances is still a challenging research topic which has received much attention. A large number of literatures were devoted to this field of research 5‐15 . Using linear matrix inequalities (LMIs) derived by different Lyapunov‐Krasovskii functionals, $$$ {\mathscr{H}}_{\infty } $$$ stability analysis are studied in References 5‐12.…”

“…A large number of literatures were devoted to this field of research 5‐15 . Using linear matrix inequalities (LMIs) derived by different Lyapunov‐Krasovskii functionals, $$$ {\mathscr{H}}_{\infty } $$$ stability analysis are studied in References 5‐12. Using the tools of invariant set analysis and Lyapunov function, sufficient conditions on robust attractor for linear delay systems in terms of LMIs are derived by Reference 13.…”