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. (C) 2016 Elsevier Ltd. All rights reserved.