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Control Theory
Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006
The observability Kalman decomposition of (A, C) is WTAW=[A10A2A3],CW=[C10],W∈ℝn×northogonal,
Intermodel Conversion
Published in S. Bingulac, Algorithms for Computer-Aided Design of Multivariable Control Systems, 2018
(1) In addition to TFRo and TFRc, other available algorithms are "classical" minimal realization procedures such as Hessenberg' s, Kalman decomposition and a Jordan form procedure. Possible sequences of algorithms are given in the table below which represent conversions from a transfer function matrix to one of the state space minimal realizations. of course, all of the resulting state space forms, SS,, have the same transfer function matrix, i.e. SS^, (SSTF) = TF,, where TF, = TF for all /= [1 ,6 ]. >
State-space linear stability analysis of platoons of cooperative vehicles
Published in Transportmetrica B: Transport Dynamics, 2019
J. Sau, J. Monteil, M. Bouroche
Let us conserve active vehicles, but now . B is a matrix with again only non 4 null elements: . The rank of the controllability matrix is now 36<40, showing that the platoon system is non-controllable. Usually, a Kalman decomposition of the state space (Astrom and Wittenmark 1997) is performed in order to separate the non-controllable subspace from the controllable one. In our case, this task is facilitated due to the already block triangular structure of the dynamic matrix and the structure of the input matrix B: it is immediate to see that the first four rows of the controllability matrix are equal to zero. This shows that the non-controllable subspace is formed by the two first drivers states, which is physically obvious.