H_∞ sliding mode based scaled consensus control for linear multi-agent systems with disturbances

This paper studies the scaled consensus control problem of networked multi-agent systems with linear coupling dynamics and external disturbances. A state feedback based distributed H_∞ sliding mode control (SMC) approach is firstly established by designing integral-type sliding function, and a linear matrix inequality (LMI) based sufficient condition is given, which can guarantee the states of all agents achieving scaled consensus with H_∞ disturbance attenuation index on sliding surface. A distributed adaptive SMC law with adaptive updated law is proposed such that the sliding surface is reachable. Then, the output feedback based distributed H_∞ SMC is considered by designing distributed observer, and a SMC law is synthesized for the reaching motion based on the state estimates. A LMI based sufficient condition for the scaled consensus with H_∞ disturbance attenuation index of the overall closed-loop system is derived. At last, the proposed distributed H_∞ SMC is further extended to solve the scaled consensus control problem of networked multi-agent systems under switching topology. An example is included to show the effectiveness of the proposed methods.