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Robust admissible consensus of singular multi‐agent systems using sliding mode approach
Author(s) -
Li Min,
Ma Shuping,
Yan Zhiguo
Publication year - 2021
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2350
Subject(s) - control theory (sociology) , mathematics , parametric statistics , linear matrix inequality , bounded function , quadratic equation , norm (philosophy) , integral sliding mode , upper and lower bounds , mathematical optimization , sliding mode control , computer science , law , nonlinear system , control (management) , mathematical analysis , statistics , physics , geometry , quantum mechanics , artificial intelligence , political science
The admissible consensus problem of singular multi‐agent systems (SMASs) with mismatched norm‐bounded parametric uncertainties and unknown norm‐bounded disturbances is investigated by an integral sliding mode technique. Under a directed spanning tree network of the state transmission graph, the error states are defined. Then a linear matrix inequality (LMI)‐based sufficient condition is presented to guarantee regularity, free impulse, quadratic stability and H ∞ performance of the sliding mode dynamics of the error states. Next, an integral sliding manifold parameter is designed to decrease the order of the LMI caused by the parametric uncertainties, and matrix inversion formulas and inequality techniques are applied to reduce the conservativeness of the LMI. Finally, the control laws, relying on the error states, the property of the state transmission graph and the upper norm bound of disturbances, are presented to ensure the state trajectories of the resulting closed‐loop system to achieve robust admissible consensus with H ∞ performance. A simulation example is provided to show the effectiveness of the proposed method.