Robust stabilization of uncertain time-delay systems containing nonlinear saturating actuators (Q2713513)

The time-delay systems NEWLINE\[NEWLINE\dot x(t)= A(t)x(t)+A_1(t)x(t-d) +B(t) u(t),\tag{1}NEWLINE\]NEWLINE are considered, where NEWLINE\[NEWLINEA(t)=A+\Delta A(t),\;A_1(t)=A_1+ \Delta A_1(t),\;B(t)=B_1+ \Delta B_1(t),NEWLINE\]NEWLINE NEWLINE\[NEWLINE\Delta A(t)= H_1F_1(t)E_1,\;\Delta A_1(t)= H_2F_2(t)E_2,\;\Delta B(t)=H_3F_3(t)E_3,NEWLINE\]NEWLINE NEWLINE\[NEWLINEF^T_i(t)F_i(t)\leq I,\;i=1, 2,3.NEWLINE\]NEWLINE An investigation is carried out with the aid of a Lyapunov-Krasovsky functional NEWLINE\[NEWLINEV\bigl[x(t), t\bigr]=x^T (t)Px(t)+ \int^0_{-d}\left[ \int^t_{t+s} x^T(\theta) R_1x(t) d\theta +\int^t_{t-d+s}x^T (\theta) R_2x (\theta) d\theta \right]ds,NEWLINE\]NEWLINE where \(P,R_1,R_2\) are positive-definite symmetric matrices.NEWLINENEWLINENEWLINESufficient conditions of stabilization of system (1) are obtained. They have the form of matrix inequalities. A numerical example is given.