Nonlinear controller design for absolute stabilization control problems

This paper discusses the absolute stabilization problem for Lur'e systems with multiple nonlinear loops in terms of state-space approach. Solvability conditions are presented to design nonlinear controllers such that the closed-loop system is absolutely stable via the algebraic matrix inequality (AMI) approach. It is shown that feedback controllers exist if and only if a class of special multilinear matrix inequalities (MLMIs) are solvable. Also, the AMI-based design method obtained in this paper is simplified so as to be computationally feasible and tractable. The approach can be generalized to deal with other problems such as H₂, H_∞ and dissipation control problem.