Fig 1

Relationship for two functions"

Fig 2

Approximation of curve $\left| {{\boldsymbol{z}}({\bf{j}}{\boldsymbol{\omega}} )} \right|$ "

Fig 3

Unstable poles for different time-delays"

Fig 4

Feasible region when ${{\boldsymbol{\tau}} _{{\boldsymbol{k0}}}} = {\boldsymbol{5}}$ "

Fig 5

Feasible region when ${{\boldsymbol{\tau }}_{{\boldsymbol{k0}}}} = {\boldsymbol{30}}$ "

Fig 6

Critical time-delay for different control parameters"

Fig 7

Frequency-sweeping curve"

Fig 8

Step response when ${\boldsymbol{\tau}} = {\boldsymbol{0.18}}\;{ {s}}$ "

Fig 9

Step response when ${\boldsymbol{\tau}} = {\boldsymbol{0.19}}\;{ {s}}$ "

Fig 10

TDS-LADRC structure for systems with time-delay"

Fig 11

Simplified diagram of TDS- LADRC systems"

Fig 12

Maximal time-delay for different ${{\boldsymbol{T}}_{\boldsymbol{m}}}$ "

Fig 13

Maximal time-delay of Theorem 3 for different ${{\boldsymbol{T}}_{\boldsymbol{m}}}$ "

Fig 14

Step response for Case A, Case B and Case C"

Fig 15

Step response for TDS-LADRC, SP-LADRC and PP-LADRC"

Table 1

Comparison for TDS-LADRC, SP-LADRC and PP-LADRC"

Fig 16

Robust test for TDS-LADRC and SP-LADRC"

Fig 17

Frequency-sweeping curves of SP-LADRC"

Fig 18

Unstable poles of SP-LADRC"