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Simple LMIs for stabilization by using delays

It is well-known that the second-order systems that cannot be stabilized by a static output feedback without a damping term, may be stabilized by inserting an artificial time-delay in the feedback. The existing Lyapunov-based methods that may treat this case and that lead to stability conditions in terms of Linear Matrix Inequalities (LMIs) suffer from high-dimensionality of the resulting LMIs. In this paper we suggest simple Lyapunov functionals that lead to reduced-order LMIs with a small number of decision variables.