The stability and control of discrete processes /
LaSalle, Joseph P.
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.
0387964118 3540964118
Control theory.
Stability.
Differential equations.
629.8312
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.
0387964118 3540964118
Control theory.
Stability.
Differential equations.
629.8312