Global convergence of interconnected pendulum-like systems

This paper is concerned with a class of discrete-time interconnected pendulum-like systems. A square matrix specifying the interconnecting structure is introduced in order to discuss the effects of nonlinear interconnections. It is shown that the global convergence of the whole interconnected system can be achieved by designing appropriate interconnect matrix. A new global optimization algorithm is presented to solve the nonlinear matrix inequalities (NMIs) arising in the synthesis problem. Numerical examples confirm the validity of the proposed algorithm and show that unstable systems can achieve global convergence through some effective interconnections.