Robust stabilization for systems with parametric uncertainty and time delay (Q5926815)

The following linear dynamical system is considered NEWLINE\[NEWLINE\dot x(t)= (A+\Delta A)x(t)+ (A_d+\Delta A_d) x(t-\tau_d)+ Bu(t),\quad \tau_d> 0,\tag{1}NEWLINE\]NEWLINE NEWLINE\[NEWLINEx(t)= \Phi(t),\qquad t\in [-\tau_d, 0],NEWLINE\]NEWLINE where NEWLINE\[NEWLINEu(t)= Kx(t)\tag{2}NEWLINE\]NEWLINE is a feedback control; the perturbations \(\Delta A\), \(\Delta A_d\) have the form NEWLINE\[NEWLINE\Delta A= B_0 FC_0,\quad\Delta A_d= B_d EC_d,\quad M_1\leq F\leq M_2,NEWLINE\]NEWLINE \(B_0\), \(C_0\), \(B_d\), \(C_d\) are fixed matrices, \(F\) is an uncertain symmetric matrix.NEWLINENEWLINENEWLINEOn the basis of a Lyapunov function, sufficient conditions for robust stabilization of the uncertain closed-loop system (1), (2), for all \(\Delta A\), \(\Delta A_d\) and \(\tau_d> 0\), are obtained.