Design of H2 (H∞)-based optimal structured and sparse static output feedback gains

This paper is devoted to the problem of designing an H2 (H∞)-based optimal sparse static output feedback (SOF) controller for continuous linear time invariant systems. Incorporating an extra term for penalising the number of non-zero entries of the static output (state) feedback gain into the optimisation objective function, we propose an explicit scheme and an iterative process in order to identify the desired sparse structure of the feedback gain. In doing so, the so-called reweighted ℓ1-norm, which is known as a convex relaxation of the ℓ0-norm, is exploited to make a convex problem through an iterative process rather than the original NP-hard problem. This paper will also show that this problem reformulation allows us to incorporate additional constraints, such as regional pole placement constraints which provide more control over the satisfactory transient behavior and closed-loop pole location, into the designing problem. Then using the obtained structural constraints, we solve the structural H2 (H∞) SOF problem. Illustrative examples are presented to show the effectiveness of the proposed approaches.