Ellipsoidal Toolbox swMATH ID: 10826 Software Authors: Kurzhanskiy, A. A.; Varaiya, P. Description: Ellipsoidal Toolbox for MATLAB. Ellipsoidal Toolbox (ET) is a standalone set of easy-to-use configurable MATLAB routines to perform operations with ellipsoids and hyperplanes of arbitrary dimensions. It computes the external and internal ellipsoidal approximations of geometric (Minkowski) sums and differences of ellipsoids, intersections of ellipsoids and intersections of ellipsoids with halfspaces and polytopes; distances between ellipsoids, between ellipsoids and hyperplanes, between ellipsoids and polytopes; and projections onto given subspaces. Ellipsoidal methods are used to compute forward and backward reach sets of continuous- and discrete-time piecewise affine systems. Forward and backward reach sets can be also computed for piecewise linear systems with disturbances. It can be verified if computed reach sets intersect with given ellipsoids, hyperplanes, or polytopes. Homepage: https://code.google.com/p/ellipsoids/ Dependencies: Matlab Related Software: SpaceEx; MPT; Flow*; ToolboxLS; XSpeed; JuliaReach; LAPACK; SLICOT; Matlab; QEPCAD; HyTech; PHAVer; KeYmaera; ElemStatLearn; Lazysets.jl; Arb; Algorithm 919; DifferentialEquations.jl; CORA; INTLAB Cited in: 37 Publications all top 5 Cited by 89 Authors 5 Kurzhanskiĭ, Aleksandr Borisovich 3 Frehse, Goran 3 Mitchell, Ian M. 3 Varaiya, Pravin Pratap 2 Bogomolov, Sergiy 2 Chirikjian, Gregory S. 2 Dumont, Guy A. 2 Forets, Marcelo 2 Kaynama, Shahab 2 Oishi, Meeko M. K. 2 Podelski, Andreas 2 Schilling, Christian 1 Abate, Alessandro 1 Adzkiya, Dieky 1 Alparslan Gök, Sırma Zeynep 1 Amigo, Isabel 1 An, Nguyen Thai 1 Arcak, Murat 1 Chen, Mo 1 Chonavel, Thierry 1 Dang, Thao 1 Dar’in, A. N. 1 Daryin, Alexander N. 1 De Schutter, Bart 1 Defterli, Ozlem 1 Devonport, Alex 1 Digailova, I. A. 1 Ding, Minghui 1 Doyen, Laurent 1 Dreossi, Tommaso 1 Dudley, Rachel 1 Erwin, Richard Scott 1 Franzè, Giuseppe 1 Goubault, Eric 1 Green, Jeremy 1 Haeri, Mohammad 1 Hamri, H. 1 Hespanha, João Pedro 1 HomChaudhuri, Baisravan 1 Iwata, Satoru 1 Jaulin, Luc 1 Johnson, Taylor T. 1 Khatibi, Mahmood 1 Kropat, Erik 1 Kühn, Christian 1 Kurzhanskiy, Alex A. 1 Larroca, Federico 1 Lazar, Mircea 1 Li, Yinong 1 Lucia, Walter 1 Lughofer, Edwin 1 Maidens, John N. 1 Matviĭchuk, Aleksandr Rostislavovich 1 Meyer, Pierre-Jean 1 Mitra, Sayan 1 Morzhin, Oleg Vasil’evich 1 Nakatsukasa, Yuji 1 Pappas, George J. 1 Parshikov, Grigoriĭ Virktorovich 1 Piazza, Carla 1 Platzer, André 1 Putot, Sylvie 1 Qin, Xiaolong 1 Rauh, Andreas 1 Rosa, Paulo 1 Shiffman, Bernard 1 Shmatkov, A. M. 1 Sijs, Joris 1 Silvestre, Carlos J. 1 Silvestre, Daniel A. M. M. 1 Takeda, Akiko 1 Tochilin, P. A. 1 Tyatyushkin, Alexander Ivanovich 1 Ushakov, Vladimir Nikolaevich 1 van Heusden, Klaske 1 Vaton, Sandrine 1 Vinod, Abraham P. 1 Viry, Frédéric 1 Vostrikov, I. V. 1 Wan, Yiming 1 Wang, Kan 1 Weber, Gerhard-Wilhelm 1 Yan, Yan 1 Ye, Hao 1 Yousefi, Mahdi 1 Zhai, Shouchao 1 Zhang, Ziwei 1 Zheng, Hao 1 Zheng, Ling all top 5 Cited in 24 Serials 4 Automatica 2 Journal of the Franklin Institute 2 Differential Equations 2 Proceedings of the Steklov Institute of Mathematics 1 International Journal of Control 1 Journal of Applied Mathematics and Mechanics 1 Geometriae Dedicata 1 Information Sciences 1 Journal of Optimization Theory and Applications 1 Systems & Control Letters 1 Information and Computation 1 International Journal of Mathematics 1 International Journal of Adaptive Control and Signal Processing 1 Automation and Remote Control 1 European Journal of Operational Research 1 SIAM Journal on Optimization 1 Computational Optimization and Applications 1 Formal Methods in System Design 1 SIAM Journal on Scientific Computing 1 International Journal of Applied Mathematics and Computer Science 1 Systems & Control: Foundations & Applications 1 Studies in Fuzziness and Soft Computing 1 Nonlinear Analysis. Hybrid Systems 1 International Journal of Systems Science. Principles and Applications of Systems and Integration all top 5 Cited in 13 Fields 30 Systems theory; control (93-XX) 8 Computer science (68-XX) 6 Numerical analysis (65-XX) 6 Operations research, mathematical programming (90-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX) Citations by Year