Stability analysis for linear non-autonomous systems with continuously distributed multiple time-varying delays and applications
New sufficient conditions for exponential stability of a nonautonomous linear system with distributed delays are given. The system has the form \[ \dot{x}(t)=A_0(t)x(t)+\sum_{i=1}^{p}A_i(t)x(t-h_i(t))+\sum_{k=1}^{q}D_k(t)\int_{t-r_k(t)}^t x(s)\,ds, \;\;t\geq0, \] where \(A_i\), \(D_k\) are given continuous matrix functions, the delay functions \(h_i\), \(r_k\) are bounded and \(dh_i/dt<1\), \(dr_k/dt<1\). The results are obtained by employing a Lyapunov-Krasovskii functional. Some conditions are presented in the form of Riccati inequalities. This gives the authors the opportunity to compute bounds that characterize the exponential stability rate of the solutions. To illustrate the usefulness of the new results, sufficient conditions for robust stability and stabilization of uncertain linear control system are obtained. Numerical examples are presented.
scientific article; zbMATH DE number 5989458