Linear Systems Theory
eBook - PDF

Linear Systems Theory

Second Edition

João P. Hespanha

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eBook - PDF

Linear Systems Theory

Second Edition

João P. Hespanha

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About This Book

A fully updated textbook on linear systems theory Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. This updated second edition of Linear Systems Theory covers the subject's key topics in a unique lecture-style format, making the book easy to use for instructors and students. João Hespanha looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization and examines advanced foundational topics, such as multivariable poles and zeros and LQG/LQR.The textbook presents only the most essential mathematical derivations and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these tools. This second edition contains a large number of new practice exercises with solutions. Based on typical problems, these exercises guide students to succinct and precise answers, helping to clarify issues and consolidate knowledge. The book's balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review.

  • Easy-to-use textbook in unique lecture-style format
  • Sidebars explain topics in further detail
  • Annotated proofs and discussions of MATLAB commands
  • Balanced chapters can each be taught in two hours of course lecture
  • New practice exercises with solutions included

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Information

Publisher
Princeton University Press
Year
2018
ISBN
9781400890088
Edition
2
Topic
Mathematics
Subtopic
Applied Mathematics
Index
Mathematics
330
INDEX
satellite
motion,
160
Schur
stable
matrix,
70,
79,
96,
191
semigroup
property,
see
state
transition
matrix
semisimple
matrix,
see
diagonalizable
matrix
sensitivity
function,
271
separation
principle,
208,
296,
304
separation
theorem,
see
separation
principle
set-point
control,
276,
297–302,
304
settling
time,
311,
312,
319
SI,
see
single-input
system
similarity
transformation,
50,
162–167,
198–202,
213–215
SIMO,
see
single-input,
multiple-output
system
Simulink,
see
MATLAB
single-input,
multiple-output
system
(SIMO),
6,
52,
193,
196
single-input,
single-output
system
(SISO),
6
single-input
system
(SI),
6
single-output
system
(SO),
6
SISO,
see
single-input,
single-output
system
sliding-mass
system,
22
Smith;
factorization,
228;
form,
226–229,
236,
240
Smith-McMillan;
factorization,
230;
form,
229–233,
236,
239–241,
243,
246,
247
SO,
see
single-output
system
spring-mass
system,
22
square
completion,
122,
172,
174,
257
stability
matrix,
69,
81,
90,
92,
105,
152,
154,
191,
257
stabilizability
test;
eigenvector,
170;
Lyapunov,
171,
173;
Popov-Belevitch-Hautus
(PBH),
171
stabilizable
system,
168–173
stabilization;
output
feedback,
207–208;
state
feedback,
155–156,
173
stabilizing
solution
to
the
ARE,
261
stable
subspace,
262,
266
standard
form
for;
uncontrollable
systems,
164,
169;
unobservable
systems,
199,
203
state
estimation,
197,
205–206
state
estimation
error,
205
state
feedback,
179,
205
state
reconstruction;
Gramian-based
in
continuous
time,
185–186;
Gramian-based
in
discrete
time,
188
state
transition
matrix,
61–63,
119,
146;
continuous
time,
57–58;
discrete
time,
60;
inverse,
58,
60;
semigroup
property,
57,
60
Stein
equation,
see
Lyapunov
equation,
discrete
time
step
response,
311,
312,
319
strict
feedback
form,
21–22,
30
strictly
proper
rational
function,
46
Taylor’s
formula,
98,
100
time
invariance,
32,
35,
36,
53
time
reversibility;
controllability/reachability,
138;
observability/constructibility,
190
time
scaling;
controllability
and
reachability,
139;
observability/constructibility,
190
time
shifting,
32;
Z
transform,
37,
41
tracking
error,
284
transfer
function;
continuous
time,
38–39,
43–44;
discrete
time,
40,
45
transmission-blocking
property,
298;
invariant
zeros,
237–238;
transmission
zeros,
232–234
transpose
of
a
vector/matrix,
8
unconstructible
subspace;
continuous
time,
182–186;
discrete
time,
187–188
uncontrollable
state
component,
165
uncontrollable
system;
continuous
time,
148
under-actuated
system,
298
undershoot,
311,
312,
319
unicycle,
29
uniformly
bounded
signal,
109
unobservable
state
component,
199
unobservable
subspace,
199;
continuous
time,
180–186;
discrete
time,
187–188
variation
of
constants
formula;
continuous
time,
59,
63,
65,
129,
180;
discrete
time,
60,
69
Z
transform,
37–38,
41–42,
44,
53;
convolution,
42;
time
shifting,
41
zero
polynomial,
230
zero-state
equivalence,
45,
50,
54,
55,
212
zero-state
response,
35
zeros;
invariant,
236–239,
249,
298;
SISO,
215,
225;
transmission,
226,
230,
232–234,
236–239,
247,
249,
250,
279–281,
297,
298

Table of contents