Analysis and control of nonlinear systems with stationary sets time-domain and frequency-domain methods (World Scientific, 2009)
Includes bibliographical references (pages 295-308) and index
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