Synthesizing a negative-imaginary system with a specified L2-performance bound via nonlinear static output feedback control

Abstract

In this paper, an iterative algorithm is proposed for synthesizing a nonlinear negative-imaginary (NI) system by designing a stabilizing nonlinear static output feedback (SOF) controller for input-affine polynomial systems. Additionally, $L_2$-performance of the closed-loop system is ensured in local sense. This scheme can handle robustness in the face of NI and $L_2$-norm bounded uncertainties of the system. Since the design of nonlinear SOF control ensuring closed-loop NI property is inherently a bilinear matrix inequality (BMI) problem, a set of sufficient conditions is derived in polynomial optimization framework using the Lyapunov-based approach with no structural constraints imposed on the Lyapunov function, contrary to the existing result. To solve this optimization problem, a computationally tractable sum of squares (SOS) decomposition technique is applied. The effectiveness of the developed results is demonstrated through numerical examples, highlighting the favorable features of the proposed synthesis scheme.