Byrnes, C. I.; Gilliam, D. S.; Shubov, V. I.; Weiss, G. Regular linear systems governed by a boundary controlled heat equation. (English) Zbl 1010.93052 J. Dyn. Control Syst. 8, No. 3, 341-370 (2002). The systems are governed by the heat equation \[ {\partial y(t, x) \over \partial t} = \Delta y(t, x) \quad (0 \leq t < \infty, \;x \in \Omega) \] in a \(n\)-dimensional domain \(\Omega\) with various inputs and outputs; for instance, Type 1 input is Neumann boundary control on part of the boundary, Type 1 output is the trace of \(y(t, x)\) on part of the boundary. The object is to show that these systems are regular in the sense of G. Weiss (see references in the paper). Reviewer: Hector O.Fattorini (Los Angeles) Cited in 1 ReviewCited in 32 Documents MSC: 93C20 Control/observation systems governed by partial differential equations 35K20 Initial-boundary value problems for second-order parabolic equations 35K05 Heat equation 93C05 Linear systems in control theory Keywords:regular linear systems; boundary control; heat equation × Cite Format Result Cite Review PDF Full Text: DOI