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
鄂公網(wǎng)安備 42010302001612號(hào) 