LMI toolbox

Linear Matrix Inequalities (LMIs) and LMI techniques have emerged as powerful design tools in areas ranging from control engineering to system identification and structural design. The LMI Control Toolbox implements state-of-the-art interior-point LMI solvers. While these solvers are significantly faster than classical convex optimization algorithms, it should be kept in mind that the complexity of LMI computations remains higher than that of solving, say, a Riccati equation. For instance, problems with a thousand design variables typically take over an hour on today’s workstations. However, research on LMI optimization is still very active and substantial speed-ups can be expected in the future. Thanks to its efficient “structured” representation of LMIs, the LMI Control Toolbox is geared to making the most out of such improvements

References in zbMATH (referenced in 1269 articles )

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  1. Echi, Nadhem; Basdouri, Imed; Benali, Hanen: A separation principle for the stabilisation of a class of fractional order time delay nonlinear systems (2019)
  2. Ali, M. Syed; Yogambigai, J.; Kwon, O. M.: Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control (2018)
  3. de Oliveira Souza, Fernando; de Oliveira, Maurício Carvalho; Martinez Palhares, Reinaldo: A simple necessary and sufficient LMI condition for the strong delay-independent stability of LTI systems with single delay (2018)
  4. Feng, Shuang; Wu, Huai-Ning: Robust adaptive fuzzy control for a class of nonlinear coupled ODE-beam systems with boundary uncertainty (2018)
  5. Gasmi, Noussaiba; Boutayeb, Mohamed; Thabet, Assem; Aoun, Mohamed: Enhanced LMI conditions for observer-based $\mathcal H_\infty$ stabilization of Lipschitz discrete-time systems (2018)
  6. Gritli, Hassène; Belghith, Safya: Robust feedback control of the underactuated inertia wheel inverted pendulum under parametric uncertainties and subject to external disturbances: LMI formulation (2018)
  7. Kusii, S. M.: Stabilization and attenuation of bounded perturbations in discrete control systems (2018)
  8. Lien, Chang-Hua; Yu, Ker-Wei; Hsieh, Jer-Guang; Chung, Long-Yeu; Chen, Jenq-Der: Simple switching signal design for $H_\infty$ performance and control of switched time-delay systems (2018)
  9. Lin, Chong; Chen, Bing; Shi, Peng; Yu, Jin-Peng: Necessary and sufficient conditions of observer-based stabilization for a class of fractional-order descriptor systems (2018)
  10. Rao, Ruofeng; Tang, Gaozhi; Gong, Jiuqi; Wan, Xiaoyan; Wu, Guanghong; Zhang, Qiao; Zhong, Shouming: Robust stability of nonlinear diffusion fuzzy neural networks with parameter uncertainties and time delays (2018)
  11. Salcedo, José V.; Martínez, Miguél; García-Nieto, Sergio; Hilario, Adolfo: Bibo stabilisation of continuous-time Takagi-Sugeno systems under persistent perturbations and input saturation (2018)
  12. Sowmiya, C.; Raja, R.; Cao, Jinde; Li, X.; Rajchakit, G.: Discrete-time stochastic impulsive BAM neural networks with leakage and mixed time delays: an exponential stability problem (2018)
  13. Syed Ali, M.; Meenakshi, K.; Gunasekaran, N.; Usha, M.: Finite-time passivity of discrete-time T-S fuzzy neural networks with time-varying delays (2018)
  14. Wang, Jun-Wei; Liu, Ya-Qiang; Sun, Chang-Yin: Pointwise exponential stabilization of a linear parabolic PDE system using non-collocated pointwise observation (2018)
  15. Wang, Yingchun; Zheng, Longfei; Zhang, Huaguang; Xie, Xiangpeng: Event-triggered fault detection filter design for nonlinear networked systems via fuzzy Lyapunov functions (2018)
  16. Xie, Xiaochen; Lam, James: Guaranteed cost control of periodic piecewise linear time-delay systems (2018)
  17. Zheng, Wei; Wang, Hongbin; Hua, Changchun; Zhang, Zhiming; Wang, Hongrui: Dynamic output-feedback control for nonlinear continuous-time systems based on parametric uncertain subsystem and interval type-2 fuzzy model (2018)
  18. Aliev, F. A.; Larin, V. B.: A note about the solution of matrix Sylvester equation (2017)
  19. Ali, M. Syed; Yogambigai, J.: Finite-time robust stochastic synchronization of uncertain Markovian complex dynamical networks with mixed time-varying delays and reaction-diffusion terms via impulsive control (2017)
  20. Asemani, Mohammad Hassan; Vatankhah, Ramin: Non-PDC observer-based T-S fuzzy tracking controller design and its application in chaos control (2017)

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