Journal ArticleDOI
Similarity transformations involving the schwarz and companion matrices
TLDR
Krylov's algorithm is used to unify and extend recent work on relating a matrix to its companion form and the companion matrix to the Schwarz form.Abstract:
Krylov's algorithm is used to unify and extend recent work on relating a matrix to its companion form and the companion matrix to the Schwarz form. A general solution to the "inverse problem of stability" is presented and illustrated.read more
Citations
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Journal ArticleDOI
Schwarz matrix properties for continuous and discrete time systems
TL;DR: A matrix analogous to the Schuarz matrix is described which is useful in studying the root distribution of a prescribed polynomial relative to the unit circle.
Journal ArticleDOI
A matrix in the block Schwarz form and the stability of matrix polynomials
TL;DR: A sufficient condition is derived for determining the stability of a multivariable system whose characteristics are expressed by a matrix polynomial whose characteristics may or may not be symmetric.
Journal ArticleDOI
Canonical form for the matrices of linear discrete-time systems
TL;DR: In this article, a canonical form for real nonderogatory convergent matrices, such as the A matrices which occur in the description of linear discrete-time dynamical systems by vector-matrix difference equations of the form xk+1 = Axk + Buk, is proposed.
Journal ArticleDOI
Canonical forms for time-invariant linear control systems: a survey with extensions Part I. Single-input case
John Maroulas,Stephen Barnett +1 more
TL;DR: In this paper, transformations of a given, completely controllable, single-input, constant linear system are described for the cases when the state matrix is to be in companion, Jordan, Schwarz, Routh or comrade form.
Journal ArticleDOI
A new representation of siso systems for studying approximated models
TL;DR: In this article, a nonlinear matrix equation is introduced and it is shown that a particular solution of the considered equation contains for SISO systems the same type of information carried in closed-loop characteristic values.
References
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Journal ArticleDOI
Optimal Bang-Bang Control With Quadratic Performance Index
W. M. Wonham,C.D. Johnson +1 more
TL;DR: In this paper, the optimal regulator problem is formulated as a scalar control function minimization problem for quadratic performance index (QPI), where the objective function minimizes the functional for the optimal index.
Journal ArticleDOI
A matrix for evaluating Schwarz's form
TL;DR: A basic transformation matrix is established by which a phase-variable form is easily converted into a Schwarz form and Kalman-Bertram's Liapunov function is simplified and Ralston's symmetric matrix formulation of the Hurwitz criterion is derived in a completely different but much more sophisticated way.
Journal ArticleDOI
A new proof of the Hurwitz stability criterion by the second method of Liapunov, with applications to "Optimum" transfer functions
Journal ArticleDOI
The companion matrix and Liapunov functions for linear multivariable time-invariant systems
TL;DR: In this article, an algorithm is developed to generate a class of matrices N which, when non-singular, reduce a constant square matrix A by a similarity transformation C = NAN−1 to the companion form.