Table 2 Symbol and its physical meaning.

\({\mathscr {I}}_m\)

A identity matrix of dimension m

\(\mathscr {P} >\) 0

\(\mathscr {P}\) is a positive definite matrix

\(\otimes\)

The Kronecker product

\(*\)

The terms derived from the omission of symmetry

\(x_i\), \(v_i\)

The state and velocity of ith agent, respectively

H1, H2, H3, F1, F2, F3

Gain matrix parameters of the estimator

\({\sigma _i}\)

The threshold parameter

\(\Omega _i\)

Adjustment parameter matrix

\(\eta _1\), \(\eta _2\), \(\eta _3\), \(\beta\), \(\vartheta _1\), \(\eta _M\)

Scalars parameter

\(\tilde{P}\), \(\tilde{Q}_1\), \(\tilde{Q}_2\)

Positive real matrices

\(\tilde{W}_1\), \(\tilde{W}_2\)

Appropriate dimensions matrix

\({\tilde{e}}_i\), \({\tilde{e}}_{fi}\)

State estimation error and fault estimation error, respectively

\({\tilde{\varepsilon }}_i\)

\({\tilde{\varepsilon }}_i = \mathrm{{col}} \{ {\tilde{e}}_i, {\tilde{e}}_{fi} \}\)

\({\bar{e}}_i\)

Consensus error

\(\varpi\)

\(\varpi = \mathrm{{col}} \{ \omega , f_{xi}, f_{xj}, f_{vj}, f_{ui}, {\dot{f}}_{xi}, {\dot{f}}_{xj}, {\dot{f}}_{vj} \}\)