非线性系统（第三版 英文版）

1 introduction

1.1 nonlinear models and nonlinear phenomena

1.2 examples

1.2.1 pendulum equation

1.2.2 tunnel-diode circuit

1.2.3 mass-spring system

1.2.4 negative-resistance oscillator1.2.5 artificial neural network1.2.6 adaptive control

1.2.7 common nonlinearities

1.3 exercises2 second-order systems

2.1 qualitative behavior of linear systems

2.2 multiple equilibria

2.3 qualitative behavior near equilibrium points

2.4 limit cycles

2.5 numerical construction of phase portraits

2.6 existence of periodic orbits

2.7 bifurcation

2.8 exercises3 fundamental properties

3.1 existence and uniqueness

3.2 continuous dependence on initial conditions andparameters

3.3 differentiability of solutions and sensitivity equations

3.4 comparison principle

3.5 exercises4 lyapunov stability

4.1 autonomous systems

4.2 the invariance principle

4.3 linear systems and linearization

4 4 comparison functions

4.5 nonautonomous systems

4.6 linear time-varying systems and linearization

4.7 converse theorems

4.8 boundedness and ultimate boundedness

4 9 input-to-state stability

4.10 exercises5 input-output stability

5.1 l stability

5.2 l stability of state models

5.3 l2 gain

5.4 feedback systems: the small-gain theorem

5.5 exercises6 passivity

6.1 memoryless functions

6.2 state models

6.3 positive real transfer functions

6.4 l2 and lyapunov stability

6.5 feedback systems: passivity theorems

6.6 exercises7 frequency domain analysis of feedback systems

7.1 absolute stability

7.1.1 circle criterion

7.1.2 popov criterion

7.2 the describing function method

7.3 exercises8 advanced stability analysis

8.1 the center manifold theorem

8.2 region of attraction

8 3 invariance-like theorems

8.4 stability of periodic solutions

8.5 exercises9 stability of perturbed systems

9.1 vanishing perturbation

9.2 nenvanishing perturbation

9.3 comparison method

9.4 continuity of solutions on the infinite interval

9.5 interconnected systems

9.6 slowly varying systems

9.7 exercises10 perturbation theory and averaging

10.1 the perturbation method

10.2 perturbation on the infinite interval

10.3 periodic perturbation of autonomous systems

10.4 averaging

10.5 weakly nonlinear second-order oscillators

10.6 general averaging

10.7 exercises11 singular perturbations

11.1 tlie standard singular perturbation model

11.2 time-scale properties of the standard model

11.3 singular perturbation on the infinite interval

11.4 slow and fast manifolds

11.5 stability analysis

11.6 exercises12 feedback control

12.1 control problems

12.2 stabilization via hinearization

12.3 integral control

12.4 integral control via linearization

12.5 gain scheduling

12.6 exercises

13 feedback linearization

13.1 motivation

13.2 input-output linearization

13.3 full-state linearization

13.4 state feedback control

13.4.1 stabilization

13.4.2 tracking

13.5 exercises14 nonlinear design tools

14.1 sliding mode control

14.1.1 motivating example

14.1.2 stabilization

14.1.3 tracking

14.1.4 regulation via integral control

14.2 lyapunov redesign

14.2.1 stabilization

14.2.2 nonlinear damping

14.3 backstepping

14.4 passivity-based control

14.5 high-gain observers

14.5.1 motivating example

14.5.2 stabilization

14.5.3 regulation via integral control

14.6 exercises

a mathematical reviewb contraction mappingc proofs

c.1 proof of theorems 3.1 and 3.2

c.2 proof of lemma 3.4

c.3 proof of lemma 4.1

c.4 proof of lemma 4.3

c.5 proof of lemma 4.4

c.6 proof of lemma 4.5

c.7 proof of theorem 4.16

c.8 proof of theorem 4.17

c.9 proof of theorem 4.18

c.10 proof of theorem 5.4

c.11 proof of lemma 6.1

c.12 proof of lemma 6.2

c.13 proof of lemma 7.1

c.14 proof of theorem 7.4

c.15 proof of theorems 8.1 and 8.3

c 16 proof of lemma 8 1

c.17 proof of theorem 11.1

c.18 proof of theorem 11.2

c.19 proof of theorem 12.1

c.20 proof of theorem 12.2

c.21 proof of theorem 13.1

c.22 proof of theorem 13.2

c.23 proof of theorem 14.6

note and references

bibliography

symbols

index