On monotone nondecreasing step responses of third-order SISO linear systems with a pair of complex poles

The paper studies single-input/single-output systems giving nonovershooting and non-decreasing step responses, which is of great significance in industry. General type, third-order linear systems are considered, i.e. those having one real pole and a pair of complex poles, with various real zero patterns. Emphasis has been put on the relations between the pole/zero locations and the desired monotone nondecreasing behaviour of the system. Sufficient conditions for various zero structured systems, together with a necessary and sufficient condition for the general system, have been derived. The sufficient conditions are tight, simple and easy to use, as would be expected by practising control engineers.