A Sum of Squares-Based Approach to Robust Nonlinear Mixed H2/H∞ Output-Feedback Control for a Class of Uncertain Polynomial Systems

This paper considers the robust nonlinear mixed H2/H∞ output-feedback control problem for a class of uncertain polynomial systems. Generally, the solvable conditions of such nonlinear output-feedback control problems are nonconvex, whose computations are challenging. By using the semidefinite programming relaxation technique based on sum of squares (SOS) decomposition, the solvable conditions of above control problem are formulated in terms of state-dependent linear matrix equality (LMI), which can be effectively solved. This conversion effectively overcomes the computational difficulties caused by the non-convexity of output-feedback H∞ control design for nonlinear systems. Furthermore, the state-observer and the controller can be designed simultaneously through a single-step SOS condition and constructed in a simple analytical form, thus reducing the computational complexity in a certain degree. In the simulation, the nonlinear mass-spring-damper system is considered to illustrate the effectiveness and feasibility of the proposed approach. The results show that the proposed method not only guarantees the stability of the system, but also has good transient performance and robust performance.