Guaranteeing passivity by output feedback gain-matrix construction

For a linear time-invariant system with equal number of inputs and outputs a simple and efficient static output feedback design procedure guaranteeing closed-loop strict passivity is proposed. Using a suitable state transformation and the Kalman-Yacubovic-Popov lemma, an essential property for the output feedback gain-matrix is obtained. It is proven that for negative signed feedback, explicit matrix bounds can be determined as lower bounds for the square output feedback gain-matrix. In the analysis, the well-known necessary and sufficient conditions that are: the system in question is minimum phase and its high frequency gain is positive definite, are also obtained as intermediate results.