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Linear control theory, splines and interpolation. (English) Zbl 0830.93056

Bowers, K. L. (ed.) et al., Computation and control IV. Proceedings of the fourth Bozeman conference, Bozeman, Montana, MT, USA, August 3-9, 1994. Boston, MA: Birkhäuser. Prog. Syst. Control Theory. 20, 269-287 (1995).
This work describes the set of splines which can be generated as outputs of a linear system in controllable canonical form and it gives a procedure for computing these splines. Polynomial splines, which are commonly used, appear as a degenerate case when the system’s open-loop matrix has repeated eigenvalues. Typically, exponential splines are obtained. The input which brings one state to another, such that the corresponding outputs are prespecified at given times \(t_k\) of a finite interval, depends linearly on these successive states. The unknown states can be computed by solving a system of linear equations which arise as regularity conditions imposed on the input at \(t_k\). Higher order derivatives of the output at the endpoints of the time intervals can also be specified in advance. The case of SISO and two inputs, two outputs systems is studied in detail.
For the entire collection see [Zbl 0819.00052].

MSC:

93C95 Application models in control theory
65D07 Numerical computation using splines
93C05 Linear systems in control theory
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