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 904 articles )

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  1. Korobov, V.I.; Lutsenko, A.V.: On the robust stabilization of one class of nonlinear discrete systems (2017)
  2. Mazko, A.G.; Kusii, S.N.: Stabilization by a measurable output and estimation of the level of attenuation for perturbations in control systems (2017)
  3. Agarwal, Neha; Kar, Haranath: New results on saturation overflow stability of 2-D state-space digital filters (2016)
  4. Ahn, Choon Ki; Shi, Peng: Strict dissipativity and asymptotic stability of digital filters in direct form with saturation nonlinearity (2016)
  5. Ahn, Choon Ki; Wu, Ligang; Shi, Peng: Stochastic stability analysis for 2-D Roesser systems with multiplicative noise (2016)
  6. Amini, Amir; Azarbahram, Ali; Sojoodi, Mahdi: $H_\infty $ consensus of nonlinear multi-agent systems using dynamic output feedback controller: an LMI approach (2016)
  7. Boulaabi, Iskander; Sellami, Anis; Ben Hmida, Fayçal: Robust delay-derivative-dependent sliding mode observer for fault reconstruction: a diesel engine system application (2016)
  8. Farnam, Arash; Mahboobi Esfanjani, Reza: Improved linear matrix inequality approach to stability analysis of linear systems with interval time-varying delays (2016)
  9. Gai, Mingjiu; Cui, Shiwei; Liu, Xiaolei: Stability analysis of a class of fractional-order neural networks (2016)
  10. Ghous, Imran; Huang, Shipei; Xiang, Zhengrong: State feedback $L_1$-gain control of positive 2-D continuous switched delayed systems via state-dependent switching (2016)
  11. Haidar, Ihab; Pasillas-Lépine, William; Chaillet, Antoine; Panteley, Elena; Palfi, Stéphane; Senova, Suhan: Closed-loop firing rate regulation of two interacting excitatory and inhibitory neural populations of the basal ganglia (2016)
  12. Manfredi, Sabato: Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture (2016)
  13. Mukaidani, Hiroaki; Xu, Hua; Dragan, Vasile: Dynamic games for Markov jump stochastic delay systems (2016)
  14. Muoi, N.H.; Rajchakit, G.; Phat, V.N.: LMI approach to finite-time stability and stabilization of singular linear discrete delay systems (2016)
  15. Niamsup, P.; Phat, V.N.: A new result on finite-time control of singular linear time-delay systems (2016)
  16. Niamsup, P.; Phat, V.N.: Robust finite-time control for linear time-varying delay systems with bounded control (2016)
  17. Pourgholi, Mahdi; Boroujeni, Elham Amini: An iterative LMI-based reduced-order observer design for fractional-order chaos synchronization (2016)
  18. Ramasamy, S.; Nagamani, G.; Zhu, Quanxin: Robust dissipativity and passivity analysis for discrete-time stochastic T-S fuzzy Cohen-Grossberg Markovian jump neural networks with mixed time delays (2016)
  19. Sharma, V.; Agrawal, V.; Sharma, B.B.; Nath, R.: Unknown input nonlinear observer design for continuous and discrete time systems with input recovery scheme (2016)
  20. Tan, Feng; Zhou, Bin; Duan, Guang-Ren: Finite-time stabilization of linear time-varying systems by piecewise constant feedback (2016)

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