Delay-induced stability of vector second-order systems via simple Lyapunov functionals

It is well known that some important classes of systems (e.g. inverted pendulums, oscillators, double integrators) that cannot be stabilized by a static output-feedback, may be stabilized by inserting an artificial time-delay in the feedback. Static output-feedback controllers have advantages over observer-based controllers in the presence of uncertainties in the system matrices and/or uncertain input/output delays, where the observer-based design becomes complicated. The existing Lyapunov-based methods that may treat the case of stabilizing delays and that lead to stability conditions in terms of Linear Matrix Inequalities (LMIs) suffer from high-dimensionality of the resulting LMIs with a large number of decision variables. In this paper, we suggest simple Lyapunov functionals for vector second-order systems with stabilizing delays that lead to reduced-order LMIs with a small number of decision variables. Moreover, differently from the existing methods, we show that the presented LMIs are always feasible for small enough delays.