Dynamic Observer-Based H-Infinity Consensus Control of Fractional-Order Multi-Agent Systems

This paper considers the H-infinity consensus control problem of fractional-order multi-agent systems (FOMASs) with external disturbances (order <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0\lt \alpha \lt 1$ </tex-math></inline-formula>) based on dynamic observer method. Using matrix spectral decomposition and the algebra properties of Kronecker product, the distributed H-infinity consensus problem in FOMASs is converted to an H-infinity problem for a group of independent fractional-order systems (FOSs) having the same dimension as that of a single agent. Based on the lemma of H-infinity stability for FOS in term of linear matrix inequalities (LMIs) and by introducing a new linearizing change of variables, the design conditions for the H-infinity consensus controller are derived. A multi-step procedure for constructing controller and dynamic observer is further presented. In the simulation part of the paper, an example of the PD<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\alpha }$ </tex-math></inline-formula>-controlled Newcastle robot model is given to illustrate the effectiveness of the theoretical results. Note to Practitioners—Due to the unique memorability of fractional-order calculus, its application to H-infinity consensus control of multi-agent systems brings system performance metrics closer to reality. This paper investigates the H-infinity consensus problem of FOMASs based on dynamic observers under disturbance. In practical applications, it is hard to directly measure the states of some FOMASs. Therefore, to solve the H-infinity consensus control problem of such systems, we introduce concepts including multi-agents, dynamic observers, and fractional-order. The primary objective is to achieve equilibrium in such FOMASs as closely to reality as possible. Optimizing system performance indicators brings the system to its desired state. Finally, an example of the PD<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\alpha }$ </tex-math></inline-formula>-controlled Newcastle robot model is provided to demonstrate the validity of the theorems.