Stability and stabilizability of dynamical systems with multiple time-varying delays: Delay-dependent criteria (Q1774463)

The linear system with delays is considered \[ \dot{x}(t)=(A+DF(t)E)x(t)+\sum_{j=1}^{p}(A_{j}+D_{j}F_{j}(t)E_{j})x(t-h_{j}(t))+ (B+D_{b}F_{b}(t)E_{b})u(t), \] where \(F(t),F_{j}(t),j=1,\dots,p \) and \( F_{b}(t) \) are bounded uncertainties matrices. Sufficient conditions of stability and stabilizability \((u(t)=Kx(t))\) for the case \(F(t)=F_{1}(t)=\dots=F_{p}(t)=0,F_{b}(t)=0\) are obtained. Moreover criteria of robust stability and stabilizability \((u(t)=Kx(t))\) are established.