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A self-contained, highly motivated and comprehensive account of basic methods for analysis and application of linear systems that arise in signal processing problems in communications, control, system identification and digital filtering.
0 v3 Q9 h: X( t* aLINEAR SYSTHNIE
& B+ z8 L! W+ q/ F; ZTHOMAS KAILATH
: p& `3 d% z9 oDepartment of Electrical Engineering. \2 a# _& Q, M' t3 x
Stanford University; ?9 `1 \! I" P) _+ i0 D( r5 L
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+ i9 P& k7 s) ~6 U1 t7 z4 `PRENTICE-HALL, INC,, Englewood Cliffs, N.J. 07632! r& z5 x! C' j L* n
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Library of Congress Cataloging in Publication Data* u" g5 O4 H3 \
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Includes bibliographies and index.2 F4 n' G2 u$ M3 W9 T; ~8 Q6 h
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+ T6 c' i8 [; U! P! t& ^C 1980 by Prentice-Hall, Inc5 D; [" @3 A4 r8 k- l
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CONTHE
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PREFACE
5 J! Y: G( g1 t, z8 T; ?) YXI[I8 q3 }4 d k8 Z: K. j- j
CHAPTER 1 BACKGROUND MATERIAL6 _- P/ U) u! J' E% S# h; ?! q
I I Some Subtleties in the Definition of linearity,) \7 i) {' e& t+ K
1.2 Unilateral Laplace Transforms and a generalized- g7 _: P+ b# v1 V. l
1.3 Impulsive Functions, Signal Representations,
" |) `2 v; g, nand Input-Output Relations, I4
9 C7 r1 T0 V5 T$ v, b1.4 Some remarks on the Use of matrices, 277 E- W" F4 \9 r
CHAPTER 2 STATE-SPACE DESCRIPTIONS-SOME) i# x" Y9 N/ o; Z6 T
BASIC CONCEPTS
: g, h) S7 W- W/ w/ m& q& Q$ W20: e% J. X3 R! j2 L* [- v8 p6 w
al realizations. 35
1 h3 j2 U1 B- H: k2.1.I Some remarks on analog computers, 35
% ?! i9 l' a+ W( i* y4 s; B2.1 2 Four canonical realizations, 37% ~0 ^2 o* N3 i |" L5 o& h
2.1.3 Parallel and cascade realizations, 45
7 b5 w( D0 e/ [9 g( l) ]Sections so marked throughout Contents may be skipped
7 r% O8 k3 j3 N& q# g
% f# ?; b$ {; B m/ v9 w* PYll2 O1 y. A7 k$ c
2.2 State Equations in the Time and fre
+ W9 o) b8 D" Q6 r22. i Matrix notation and state space equations, 50- c- H7 r, R! ]: ]% W
22.2 obtuinii
" I( r& A2 p" ?" X, n- K7 l& _乎 lions directy--s0me
5 W# Q8 s$ f: A* R9 Texamples, linearization, 55( `# V, E. X: R, `" t! _
2. 2.3 A definition of state, 62
3 Y; W" o2 g9 x0 y% |+ \3 G& |a2.4 More names and definitions,66' Q! X i# F. ?' j. C" }
2.3 Initial Conditions for Analog-Computer simulation
: ~0 `% k# {$ j4 r" MObservability and Controllability for Continuous
+ |) f5 w d3 C( l5 Q; W2 E$ `7 xand discrete- Time realizations , 799 o. m9 X0 L2 j4 z6 J' O. G; s- `2 U
2.3I Determining the initial conditions,szare, a9 q+ I8 F9 w* [1 H
23. 2 Setting up initial conditions, state controllability, &4% W4 m9 L O% [, _
23.3D
5 z4 }! q: g7 q' X# b) xbility, 904 z# [% N! e% p: l: N7 ?
23.4S
3 a5 u8 s; \: A' }7 }2. 4 Further Aspects of Controllability and obs
" i7 Z+ R3 M& z" mty,20' Y5 q! j, U# o. N# s
2.4I Joins observability and controlability, the uses- _: R( v7 P( v8 g
diagonal forms, 120
4 t' |2 f9 r; S- J/ w" P. ]3 _2 Standard forms for noncontrollable andor
+ K {% M" a0 [% B+ ^nonobservable sy stems, 728$ Y5 S5 a6 K" L$ ~+ X
2.4.3 The PapoyBelevirch-Hautus tests for+ p4 d0 V9 c2 s: x' q
controllability and observability, 13.56 C' D2 K# v2 \' J4 X7 C' S8 @% ]
R2.4.4 Some tests for relatively prime polynomials, 140; p: f7 t' ~( f5 s' {% |
2. 4,5 Some worked exan1 T6 t* d# ~5 A( T& G/ T
*2.5 Solutions of state Equations and modal+ L# d1 x' I6 u. i! _. W
Decompositions, 160
& w1 w* `' O- b8 v1 P8 }. P2.5.1 Time-invariant equations and matrix
0 p9 [' S* ~0 [1 k. z! Wexponentials, 162
* `+ S. e) b5 c" f5 X, N$ S2.5.2 Modes of oscillation and modal decompositions, 1680 |2 H' ^1 u9 _, v: s
2.6 A Glimpse of Stability Thcory, 17
' K; p* A' F" u; i, L2, 6.2 The Lyapunov criterion, I775 h1 r5 i6 X# y$ C" A1 r7 y1 L
26.1E
2 T; h" R$ e8 Ol stability' [& u4 M! a' V' Y4 J6 w/ Y& t: a
75
" |& n4 q6 `1 ]0 [! o2.5.3 A stability resuit for linearised systems, 1802 m4 g7 G' T. v1 O0 ?, y0 s
CHAPTER 3 LINEAR STATE-VARIABLE FEEDBACK
K: X. Y! N. g: Y3.0 Introduction, 187/ @* y! o2 {# S) c4 [
3.1 Analysis of Stabilization by Output Feedback 188+ [5 s/ f1 l6 f9 L0 o- \" s
3. 2 State-Variable Feedback and Modal Controllability, 7970 }. l' @# C6 k. g; K7 ?
3. 2. Some formulas for the* Y, s0 J, w8 i+ N7 Y+ w
3.2.2 A transfer function approach, 202& g; [" I. m m" h1 h5 V) S5 U: f
3 Some aspects of state-yariable feedback, 204
1 ]3 ?4 t7 Z* _; w- F$ G0 v d7 f1 r5 i7 R9 p' l
3, 3 Some worked Examples, 209: W/ D2 M, ]/ ^1 x/ ~& T
4 Quadratic Regulator Theory for ContinuousTime- W2 k u# d# ]. l0 p8 Q* w
Systems, 218
; Q" r8 V5 Q& f$ |3.4,7O9 A0 G. ]& \# r1 }
ite solut
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# C& U4 X; e5 r" T+ ~" [% q! M*3.4.2 Plausibility of the selection rule for the optima& a9 s: r! w H* q7 Y8 J
*3.4.3 The algebraic Riccati equation, 230
( L; u/ ?% k$ a. z3 u! T- S( e3.5 Discrcto-Time Systems, 2
& g8 M) ]& O9 _0 p3 Y8 S! u( v% }5 W3.5.1 Modal controlability, 238
* z- p: M0 H0 k: ? @' L. `3.5.2 Controllability to the origin, state-pariable8 m. \) }5 X0 V/ \3 D' L; y
e principle of optimality, 239
, \& C6 g7 E: \*3.5.3 The diserele-lime quadratic regulator problem, 243: q% @! c! X% |9 v; ]$ S: F8 `" t
*3.5.4 Square-root and related algorithms, 245
! B2 w( I+ V3 l+ I$ V9 t5 ZCHAPTER 4 ASYMPTOTIC OBSERVERS AND5 M7 m- r! m. x5 }2 C T
COMPENSATOR DESIGN
. q( }5 p. }- ~9 Z {) O2594 q# L4 h* f0 v7 Q/ V9 T
4.0 Introduction, 259
7 p8 d2 {/ d- m, w. t7 V4.1 Asymptotic Observers for State Measurcment, 250
~5 d" l3 E; t4.2 Combined Obscrvcr-Controllcr Compensators, 268: A0 C7 N( K. M' [8 U2 X
4.3 Rcduced-order observers 2815 k# m; | r& C0 ~( \7 C
4.4 An Optimality Critcrion for Choosing Observer Poles, 2936 E8 `, @1 r) _+ Q$ ?) Z' B8 a! m
4.5 Direct Transfer Function Design Procedures, 297
6 Q; W* A' @% b: a7 f3 F3 j! L4.5,I A transfer function reformulation of the
2 k# L- \6 l: ozer design, 298
5 A. O9 K+ V* c: ^4.5.2 Some variants of the observer-controller design, 304
( [1 Q, o: q& s5 h! l/ W+ M" q4.5.3 Design via polynomial equationf, 306; K7 U# H$ a* d& W @) P+ [
CHAPTER 5 SOME ALGEBRAIC COMPLEMENTS
2 X! U3 ~2 j4 G8 q314$ n4 L4 f3 C% M: v+ ]
5.0 Introduction. 314
0 m) {% K% G$ f& k0 p, Z5.1 Abstract Approach to State -space Realization+ W1 E- z1 ^, |; r s# l$ j
Methods; Nerode Equivalence, 315$ h5 Z# \" n! T8 h2 z
5.1.1 Realis
" h4 Y9 u% v" B. Y/ Y! j ~) dcov parame
! M3 Z! }1 m1 t& d! U5.2 Geometric Interpretation of Similarity Transformations, a! m$ I/ l0 \( Y$ x
Linear vector Spaces, 3290 T: i& } r4 c, z1 X, `- @
5.2. Vectors in n-space: linear independence, 3305 e; ~- C' ?7 E) B( }& i
5.2.2 Matrices and transformations, 333
- A% M$ Z( r' C5.2.3 Vector subspaces, 338
# U' T7 \1 N! w2 q0 \& i' L5.2 4 Abstract linear vector spaces, 341
) Z) l: e# L1 l
5 T1 D% `9 f1 k$ x4 m- k3 P& P: bCHAPTER 6 STATE-SPACE AND MATRIX-FRACTION
: D% v& q) B/ w. \% @DESCRIPTIONS OF MULTIVARIABLE
" V# S; h+ u8 ]. M) y+ B8 ISYSTEM
, l# ~. Z3 `( e1 |7 F9 \5 P& g345; p3 r$ u+ b9 s8 {9 w
6.0 Introd5 a: P. w! x0 ?, F+ u
61 Some Direct realizations of multivarable transfer
^) Q% C3 l% W+ k% I& x6.2 State Observability and Controllability8 f/ x' e+ }0 e7 |
Matrix-Frection Descriptions, 3521 e4 ~1 ]: h0 o
62. The observability and controllability matrices, 353 i& N4 ]8 ?6 `" @5 F3 ~6 A: v
6.2.2 Standard forms for noncontrollable nonobservable2 ^7 c, h5 x( K5 Z+ ]: Q
Ins minimal realizations. 360# y2 t7 |. D* _8 c: j; G$ v/ y
6. 2. 3 Mairixfrcction description, 367, r) A3 J7 n/ y) _" r3 ]
6.3 Some pr- {* ^- _" B; a' j+ q4 l
6.3.2 Unimodular matrices, the Hermite form and- c4 f$ T% K) M/ R' I
coprime polynomial matrices, 3732 L( [0 A) J0 \8 ^( i- I, d* u: I) y
632
5 O a; ^. H4 R: j9 e* v) gd some7 Y7 x, k2 ^. J0 N7 D
application, 382 u* b7 m C6 c$ {5 ?7 W& T
63.3 The Smith form and related results, 390' M% f0 j* U* c+ }- v
rix pencils, and Kronecker form, 393
) A3 \( X/ c: W8 `4 |' l8 I- o6.4 Some Basic Sta: e-Space Realizations, 403+ h9 M8 ]& O5 r% J; }6 F/ K
64.i; [3 u0 k/ ^2 [$ `4 u* r: ~
form realizations from right MFDs, 403
5 h/ p8 b% F$ c8 ~/ biler fo( u+ E4 q9 M. C ]9 G/ \0 L
lization 408
3 G$ ?- i0 \! a7 {: R0 p6.4.5 Observer form realizations from left MFDs, 413
8 Y0 e2 ^# k* |; ^. e6.4.4 Controllability- and observability form realizations, 4.17" L e# |( c' p8 E/ O2 }
6.4.5 Canonical state-space realizations and canonical
% l( `: z8 f/ ~6.4.6 Transformations of state-space realizations, 424
0 G( ^; L6 }2 b2 t6.5 Some Properties of Rational Matrices, 439
0 I f9 n' W2 @) F5 _6.5.1 Irreducible MFDs and minimai realizations, 439, D: K6 ]. k J. D8 Z* C/ q( f
6.5.2 The Smith-McMillan form ofH(s), 443
1 B7 K5 ~9 U; J9 N: z" U( D8 A: L6.5.3 Poles and zeros of multivariable transfer functions, 4465 H& O7 [* s( J( Q% [
6.5.4 Nullspace structure, minimal polynomial bases
& R8 I2 ~1 v* N n, Cand Kronecker indices, 4555 y5 e3 Y0 p" j* j1 [
*6.6 Ncode eg* K6 u2 r7 U/ Z3 D& d
ble Systems, 470
; ?+ X3 W2 m0 X- G" R" d6.7 Canonical Matrix-Fraction and State-space' p, g: b; T, d, g+ y
6.7.1 Hermite-form MFDs and scheme I siaie-space' s( u. _$ \8 l0 a2 J' c# |8 y
67,2Pc. ?5 K& i% X) ^& X# n- K8 l, d
nialechelon mFd
5 F: z- s+ w5 G( q, @1 C! Z3 DScheme i realizations, 48.76 Y, o; R2 o- G) `" P
*6.7.3 The formal definition of canonical form, 4920 p& s! s9 x6 I, ~8 F" I
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