Analysis and control of nonlinear systems with stationary sets : time-domain and frequency-domain methods

Cover.
Contents.
Preface.
Notation and Symbols.
1. Linear Systems and Linear Matrix Inequalities.
1.1 Controllability and observability of linear systems.
1.1.1 Controllability and observability.
1.1.2 Stabilizability and detectability.
1.2 Algebraic Lyapunov equations and Lyapunov inequalities.
1.2.1 Continuous-time algebraic Lyapunov equations.
1.2.2 Continuous-time Lyapunov inequalities.
1.2.3 Discrete-time algebraic Lyapunov equations and inequalities.
1.3 Formulation related to linear matrix inequalities.
1.3.1 Schur complements.
1.3.2 Projection lemma.
1.4 The S-procedure.
1.4.1 The S-procedure for nonstrict inequalities.
1.4.2 The S-procedure for strict inequalities.
1.5 Kalman-Yakubovi183;c-Popov (KYP) lemma and its general- ized forms.
1.6 Notes and references.
2. LMI Approach to H1 Control.
2.1 L1 norm and H1 norm of the systems.
2.1.1 L1 and H1 spaces.
2.1.2 Computing L1 and H1 norms.
2.2 Linear fractional transformations.
2.3 Redheffer star product.
2.4 Algebraic Riccati equations.
2.4.1 Solvability conditions for Riccati equations.
2.4.2 Discrete Riccati equation.
2.5 Bounded real lemma.
2.6 Small gain theorem.
2.7 LMI approach to H1 control.
2.7.1 Continuous-time H1 control.
2.7.2 Discrete-time H1 control.
2.8 Notes and references.
3. Analysis and Control of Positive Real Systems.
3.1 Positive real systems.
3.2 Positive real lemma.
3.3 LMI approach to control of SPR.
3.4 Relationship between SPR control and SBR control.
3.5 Multiplier design for SPR.
3.6 Notes and references.
4. Absolute Stability and Dichotomy of Lur'e Systems.
4.1 Circle criterion of SISO Lur'e systems.
4.2 Popov criterion of SISO Lur'e systems.
4.3 Aizerman and Kalman conjectures.
4.4 MIMO Lur'e systems.
4.5 Dichotomy of Lur'e systems.
4.6 Bounded derivative conditions.
4.7 Notes and references.
5. Pendulum-like Feedback Systems.
5.1 Several examples.
5.2 Pendulum-like feedback systems.
5.2.1 The first canonical form of pendulum-like feedback system.
5.2.2 The second canonical form of pendulum-like feed- back system.
5.2.3 The relationship between the 175;rst and the second forms of pendulum-like feedback systems.
5.3 Dichotomy of pendulum-like feedback systems.
5.3.1 Dichotomy of the second form of autonomous pendulum-like feedback systems.
5.3.2 Dichotomy of the first form of pendulum-like feed- back systems.
5.4 Gradient-like property of pendulum-like feedback systems.
5.4.1 Gradient-like property of the second form of pendulum-like feedback systems.
5.4.2 Gradient-like property of the first form of pendulum-like feedback systems.
5.5 Lagrange stability of pendulum-like feedback systems.
5.6 Bakaev stability of pendulum-like feedback systems.
5.7 Notes and references.
6. Controller Design for a Class of Pendulum-like Systems.
6.1 Controller design with dichotomy or gradient-like property.
6.1.1 Controller design with dichotomy.
6.1.2 Controller design with gradient-like property.
6.2 Controller design with Lagrange stability.
6.3 Notes and references.
7. Controller Designs for Systems with Input Nonlinearities.
7.1 Lagrange stabilizing for systems with input nonlinearities.
7.2 Bakaev stabilizing for systems with input nonlinearities.
7.3 Control for systems with input nonlinearities guaranteeing di.