Linear Matrix Inequalities in Control Systems
with Uncertainty

Polyak, B. T.; Khlebnikov, M. V.; Shcherbakov, Pavel

doi:10.1134/s000511792101001x

Cited by 23 publications

(14 citation statements)

References 102 publications

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“…For minimization problem, the minimization result is equivalent under non-strict LMI constraints and strict LMI constraints. 29,30 where e P = P=e. The proof is finished.…”

Section: Construction Of Nonlinear State Space Model Of Systemmentioning

confidence: 99%

Robust stabilization for a class of complex production process systems based on multi-dimensional moving pattern

Liu

et al. 2023

Measurement and Control

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This paper studies robust stabilization problem and state feedback controller design problem for a class of complex production process systems by pattern class variable instead of state variable or output variable. Firstly, the maximum entropy clustering method is introduced and modeling method based on multi-dimensional moving pattern is given. Nonlinear state space models of systems with input-delay are established by using the trajectories of pattern class variable. Then sufficient conditions for robust stabilization of the system are obtained by Linear Matrix Inequality. In addition, a state feedback controller is designed based on this condition. Finally, the effectiveness of the methods is illustrated by taking the actual working conditions data as an example.

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“…For minimization problem, the minimization result is equivalent under non-strict LMI constraints and strict LMI constraints. 29,30 where e P = P=e. The proof is finished.…”

Section: Construction Of Nonlinear State Space Model Of Systemmentioning

confidence: 99%

Robust stabilization for a class of complex production process systems based on multi-dimensional moving pattern

Liu

et al. 2023

Measurement and Control

View full text Add to dashboard Cite

show abstract

“…Under Assumptions 1 and 2, the distributed estimator (13) and the coordinated control law (19), which depends on ( 16) and (17), can guarantee that the attitude tracking error of the follower spacecraft asymptotically converges to zero. Remark 4: The form of LMI ( 28) is inspired by (Polyak et al 30 ). Similar to the analysis in Remark 3, the corresponding solutions 3 , 4 and 5 can be obtained by the mature solution method of linear matrix inequality (Last 31 ).…”

Section: Assumptionmentioning

confidence: 99%

Distributed coordinated attitude tracking control of spacecraft formation with dynamic leader under communication delays

Zhou

Zhang

Wang

2022

Preprint

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This paper is dedicated to the challenging issue of the cooperative attitude tracking control of spacecraft formations under communication delays. A state estimator using the attitude information of the neighbors is designed for each follower spacecraft to estimate the time-varying attitude information of the leader spacecraft in the case that the leader spacecraft cannot directly communicate with all following spacecraft. By constructing auxiliary variables based on estimated values and proposing a fixed-time control law to ensure that the auxiliary variables of the spacecraft can reach zero in fixed time, which is independent of the initial state, the effects of time-varying reference attitudes on the system can be reduced. The attitude error and the estimation error are proven to converge to the region containing the origin by input-to-state stability theory combined with the Lyapunov-Krasovskii approach. To further illustrate the effectiveness of the proposed control algorithm, numerical simulation results are presented.

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“…The form of LMI ( 28 ) is inspired by (Polyak et al 27 ). Similar to the analysis in Remark 3, the corresponding solutions , and can be obtained by the mature solution method of linear matrix inequality (Last 28 ).…”

Section: Coordinated Attitude Tracking Control With a Dynamic Leader ...mentioning

confidence: 99%

Distributed coordinated attitude tracking control of a multi-spacecraft system with dynamic leader under communication delays

Zhou

Zhang

Wang

2022

Sci Rep

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This paper is dedicated to the challenging issue of the cooperative attitude tracking control of a multi-spacecraft system under communication delays. A state estimator using the attitude information of the neighbors is designed for each follower spacecraft to estimate the time-varying attitude information of the leader spacecraft in the case that the leader spacecraft cannot directly communicate with all following spacecraft. By constructing auxiliary variables based on estimated values and proposing a fixed-time control law to ensure that the auxiliary variables of the spacecraft can reach zero in fixed time, which is independent of the initial state, the effects of time-varying reference attitudes on the system can be reduced. The attitude error and the estimation error are proven to converge to the region containing the origin by input-to-state stability theory combined with the Lyapunov–Krasovskii approach. To further illustrate the effectiveness of the proposed control algorithm, numerical simulation results are presented.

show abstract

Linear Matrix Inequalities in Control Systems with Uncertainty

Cited by 23 publications

References 102 publications

Robust stabilization for a class of complex production process systems based on multi-dimensional moving pattern

Robust stabilization for a class of complex production process systems based on multi-dimensional moving pattern

Distributed coordinated attitude tracking control of spacecraft formation with dynamic leader under communication delays

Distributed coordinated attitude tracking control of a multi-spacecraft system with dynamic leader under communication delays

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