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- W2072954553 abstract "We investigate the theoretical properties of a structural form for higher-index, linear time varying semistate systems x′ = A(t)x + B(t)u + ƒ 1 (t) , 0 = C(t)x + D(t)u + ƒ 2 (t) , where D ( t ) is singular but has constant rank for all t ∈ [0, T ]. Many systems of interest in circuit and control theory exhibit the form discussed, in particular circuits with differentiators and linear-quadratic regulator problems with higher-order singular arcs. In addition to the semiexplicit structure, the systems we describe are characterized by a block upper Hessenberg coefficient A ( t ), a zero pattern in C ( t ) and B ( t ), and an invertibility condition on the components of C , B , and the subdiagonal blocks of A . We show that there exists a coordinate system in which the Hessenberg form is equivalent to a semiexplicit index-1 system embedded between two linear chains of differentiators. In a companion paper, we establish the convergence and stability of backward differentiation formulas ( BDF ) applied to the index-4 Hessenberg form, extending the theory for the index-2 and index-3 special cases." @default.
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- W2072954553 date "1988-01-01" @default.
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- W2072954553 title "A structural form for higher-index semistate equations. I. theory and applications to circuit and control theory" @default.
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- W2072954553 doi "https://doi.org/10.1016/0024-3795(88)90164-4" @default.
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