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This paper investigates the finite-time leader-following consensus problem for multi-agent systems with switching topologies. First of all, consider the characteristic of failures, a failure distribution model which is more in line with the actual situation is established, and a semi-Markov chain is used to describe the topology switching of the multi-agent system, in which the transfer rate is time-varying. Secondly, based on the past state information, a topology-dependent consensus protocol is established, then the fault-tolerant consensus problem of leader-following multi-agent is transformed into the issue of system stability, according to the mode-dependent Lyapunov function and the finite time stochastic theorem, the sufficient conditions for the stability of the closed-loop system and the constraints of average residence time are obtained. In addition, an initial-state based $ {H_\infty } $ H ∞ performance index is proposed to reduce the influence of zero initial conditions on the system. Finally, a numerical example is provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article investigates the output fault‐tolerant consensus problem for multi‐agent systems with switching topology and deception attacks. In order to reduce the effects of switching topology, the differences between topologies can be modeled as topology uncertainties. In practice, the deception attack may occur in a random way and assumed to satisfy Bernoulli distributions. The purpose of this research is to design an output fault‐tolerant controller such that, in the presence of switching topology, actuator faults, and deception attacks, the finite‐horizon output fault‐tolerant consensus can be achieved under a prespecified H∞$$ {H}_{\infty } $$ performance. An initial‐state‐based performance requirement is constructed, and this bypasses the need for the zero initial condition in the conventional H∞$$ {H}_{\infty } $$ theory. After this, the controller gains are computed by employing an iterative linear matrix inequality scheme. Finally, a numerical example is provided to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]