Stabilization by using artificial delays: An LMI approach

Static output-feedback stabilization for the nth order vector differential equations by using artificial multiple delays is considered. Under assumption of the stabilizability of the system by a static feedback that depends on the output and its derivatives up to the order n−1, a delayed static output-feedback is found that stabilizes the system. The conditions for the stability analysis of the resulting closed-loop system are given in terms of simple LMIs. It is shown that the LMIs are always feasible for appropriately chosen gains and small enough delays. Robust stability analysis in the presence of uncertain time-varying delays and stochastic perturbation of the system coefficients is provided. Numerical examples including chains of three and four integrators that are stabilized by static output-feedbacks with multiple delays illustrate the efficiency of the method.