Robust stabilization of uncertain input-delayed systems using reduction method (Q5926181)

One considers the problem of feedback stabilization of the uncertain system NEWLINE\[NEWLINE\dot x= (A+\Delta A(t)) x(t)+ \sum^r_0 B_i u_i(t- h_i)+ \sum^r_0 \Delta B_j(t) u_j(t- \widetilde h_j)NEWLINE\]NEWLINE with NEWLINE\[NEWLINEA(t)= DF(t)E,\quad B_j(t)= D_jF_j(t) E_j,\quad|F(t)|\leq 1,\quad|F_j(t)|< 1.NEWLINE\]NEWLINE The procedure is as follows: first the linear transformation NEWLINE\[NEWLINEz(t)= x(t)+ \sum^r_0 \int^t_{t- h_i} e^{A(t- h_i-\theta)} B_iu_i(\theta) d\thetaNEWLINE\]NEWLINE is used, then the robustly stabilizing feedback is designed using an appropriate quadratic Lyapunov functional.