The stability and control of discrete processes /
J.P. LaSalle.
- New York ; London : Springer Verlag, 1986.
- 150 p. ; 24 cm. + pbk.
- Applied mathematical sciences ; v. 62 .
- Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 62. .
Includes bibliographical references (p. 147) and index.
Introduction -- Liapunov's direct method -- Linear systems x' = Ax. -- An algorithm for computing An. -- A chararacterization of stable matrices. Computational criteria. -- Liapunov's characterization of stable matrices. A Liapunov function for x' = Ax. -- Stability by the linear approximation. -- The general solution of x' = Ax. The Jordan Canonical form. -- Higher order equations. The general solution of u(z)y = 0. -- Companion matrices. The equivalence of x' = Ax and u(z)y = 0. -- Another algorithm for computing An. -- Nonhomogeneous linear system x' = Ax + f(n). Variation of parameters and undetermined coefficients. -- Forced oscillations. -- Systems of higher order equations P(z)y = 0. The equivalence of polynomial matrices. -- The control of linear systems. Controllability. -- Stabilization by linear feedback. Pole assignment. -- Minimum energy control. minimal time-energy feedback control. -- Observability. Observers. State estimation. Stabilisation by dynamic feedback.
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Control theory. Stability. Differential equations.