Nonlinear Control Sy.. - Free

INDEX
discrete-time, 132
nonautonomous, 113
Magnetic suspension system, 23, 271
Mass-spring system, 1
Matrices, 39
inverse, 39
orthogonal, 39
skew symmetric, 39
symmetric, 39
transpose, 39
Matrix norms, 48
Mean-value theorem, 52
Memoryless systems, 162
Metric spaces, 32
Minimum phase systems, 285
Minkowski's inequality, 38
Neighborhood, 44
Node, 11
stable, 12
unstable, 13
Nonautonomous systems, 107
Nonlinear observability, 296
Nonlinear observers, 291
Nonlinear systems
first order., 5
linearization, 99
Normed vector spaces, 37
Observability
linear systems, 292
nonlinear, 296
Observer
Lipschitz systems, 301
with linear error dynamics, 298
Observers, 291
Open set, 44
Partial derivatives, 50
Passive system, 205, 227
351
interconnections, 208
Passivity, 201
of linear time-invariant systems, 214
theorem, 211
Passivity and small gain, 210
Perturbation analysis, 122
Phase-plane analysis, 8
Poincare-Bendixson theorem., 21
Positive definite functions, 69
decrescent, 110
discrete-time, 131
time dependent, 110
Positive real rational functions, 217
Positive system, 207
Quadratic forms, 41
Radially unbounded function, 78
Rayleigh inequality, 43
Region of attraction, 93
Relative degree, 277
Riccati equation, 246
Saddle, 13
Schwarz's inequality, 204
Second order nonlinear systems, 8
Sequences, 45
Sets, 31
Small gain theorem, 171
Stability
input-to-state, 183
of dissipative systems, 237
State vector, 3
Static systems, 162
Storage function, 225
Strange attractor, 21
Strict feedback systems, 148
Strictly output-passive system, 228
Strictly passive system, 206, 228
Strictly positive real rational functions, 217
Strictly positive system, 207