A Lyapunov-based small-gain theorem for interconnected switched systems

Nonlinear system;interconnected system;switched system;small-gain theorem;Lyapunov function

Yang, Guosong ; Liberzon ; Daniel M.

关键词: Nonlinear system;    interconnected system;    switched system;    small-gain theorem;    Lyapunov function;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/45522/Guosong_Yang.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input-to-state stable (non-ISS). We have shown that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic stability (GAS) of the interconnected system. For each switched system, with the constraints on the switching signal being modeled by an auxiliary timer, a correspondent hybrid system is defined to enable the construction of hybrid ISS Lyapunov functions. Apart from justifying the ISS property of their corresponding switched systems, these hybrid ISS Lyapunov functions are then combined to establish a Lyapunov-type small-gain condition which guarantees that the interconnected system is globally asymptotically stable.