Robust admissible consensus of singular multi‐agent systems using sliding mode approach

Abstract

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.

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

“…The related basic theories of descriptor systems have been established in [1][2][3][4]. More recently, the admissible consensus problem of descriptor multi-agent systems was investigated in [5]. In many practical situations, such as constrained robot network, the number of variables and equations in systems are inconsistent.…”

Interval observer‐based consensus control of discrete‐time multi‐agent systems under stealthy attacks

“…As a central problem in multi-agent systems, consensus is to design a protocol that makes each subsystem achieve some agreements among the system states. Consensus control has always been a hot issue, and lots of remarkable results have been achieved in both theoretical research and practical application [3][4][5][6][7].…”

Closed‐loop consensus control of partial difference multi‐agent systems via variable gain iterative learning strategy

“…9 Under these conditions, many research results on consensus control of MASs have appeared, and these results can be divided into three different aspects. 10 For example, they include continuous or discrete system model, 11,12 centralized or distributed control protocol, 13,14 fixed or switched communication topology. 15,16 In addition, the stability of the MASs is the basis to ensure the acceleration and accurate consensus control.…”