Preface -- Contents -- Chapter 1 Regularly and singularly perturbed systems -- 1.1 Regularly perturbed systems -- 1.1.1 Nonlinear nominal system -- 1.1.2 Linear nominal system -- 1.1.3 Vanishing perturbation -- 1.1.4 Nonvanishing perturbation -- 1.2 Singularly perturbed systems -- 1.2.1 Singular perturbation -- 1.2.2 Two-time-scale motions -- 1.2.3 Boundary-layer system -- 1.2.4 Stability analysis -- 1.2.5 Fast and slow-motion subsystems -- 1.2.6 Degree of time-scale separation -- 1.3 Discrete-time singularly perturbed systems -- 1.3.1 Fast and slow-motion subsystems -- 1.3.2 Degree of time-scale separation -- 1.4 Notes -- 1.5 Exercises -- Chapter 2 Design goal and reference model -- 2.1 Design goal -- 2.2 Basic step response parameters -- 2.3 Reference model -- Reference model design -- Reference model with arbitrary system type -- 2.4 Notes -- 2.5 Exercises -- Chapter 3 Methods of control system design under uncertainty -- 3.1 Desired vector field in the state space of plant model -- 3.2 Solution of nonlinear inverse dynamics -- 3.3 The highest derivative and high gain in feedback loop -- 3.4 Differentiating filter and high-gain observer -- 3.5 Influence of noise in control system with the highest derivative -- 3.6 Desired manifold in the state space of plant model -- 3.7 State vector and high gain in feedback loop -- 3.8 Control systems with sliding motions -- 3.9 Example -- 3.10 Notes -- 3.11 Exercises -- Chapter 4 Design of SISO continuous-time control systems -- 4.1 Controller design for plant model of the 1st order -- 4.1.1 Control problem -- 4.1.2 Insensitivity condition -- 4.1.3 Control law with the 1st derivative in feedback loop -- 4.1.4 Closed-loop system properties -- 4.2 Controller design for an nth-order plant model -- 4.2.1 Control problem -- 4.2.2 Insensitivity condition.

4.2.3 Control law with the nth derivative in the feedback loop -- 4.2.4 Fast-motion subsystem -- 4.2.5 Slow-motion subsystem -- 4.2.6 Influence of small parameter -- 4.2.7 Geometric interpretation of control problem solution -- 4.3 Example -- 4.4 Notes -- 4.5 Exercises -- Chapter 5 Advanced design of SISO continuous-time control systems -- 5.1 Control accuracy -- 5.1.1 Steady state of fast-motion subsystem -- 5.1.2 Steady state of slow-motion subsystem -- 5.1.3 Velocity error due to external disturbance -- 5.1.4 Velocity error due to reference input -- 5.1.5 Control law in the form of forward compensator -- 5.2 Root placement of FMS characteristic polynomial -- 5.2.1 Degree of time-scale separation -- 5.2.2 Selection of controller parameters -- 5.2.3 Root placement based on normalized polynomials -- 5.3 Bode amplitude diagram assignment of closed-loop FMS -- 5.3.1 Block diagram of closed-loop system -- 5.3.2 Bode amplitude diagram of closed-loop FMS -- 5.3.3 Desired Bode amplitude diagram of closed-loop FMS -- 5.3.4 Selection of controller parameters -- 5.4 Influence of high-frequency sensor noise -- 5.4.1 Closed-loop system in presence of sensor noise -- 5.4.2 Controller with infinite bandwidth -- 5.4.3 Controller with finite bandwidth -- 5.5 Influence of varying parameters -- 5.5.1 Influence of varying parameters on FMS and SMS -- 5.5.2 Michailov hodograph for FMS -- 5.5.3 Variation of FMS bandwidth -- 5.5.4 Degree of control law differential equation -- 5.5.5 Root placement of FMS characteristic polynomial -- 5.6 Bode amplitude diagram assignment of open-loop FMS -- 5.7 Relation with PD, PI, and PID controllers -- 5.8 Example -- 5.9 Notes -- 5.10 Exercises -- Chapter 6 Influence of unmodeled dynamics -- 6.1 Pure time delay -- 6.1.1 Plant model with pure time delay in control -- 6.1.2 Closed-loop system with delay in feedback loop.

6.1.3 Fast motions in presence of delay -- 6.1.4 Stability of FMS with delay -- 6.1.5 Phase margin of FMS with delay -- 6.1.6 Control with compensation of delay -- 6.1.7 Velocity error with respect to external disturbance -- 6.1.8 Example -- 6.2 Regular perturbances -- 6.2.1 Regularly perturbed plant model -- 6.2.2 Fast motions in presence of regular perturbances -- 6.2.3 Selection of controller parameters -- 6.2.4 Control with compensation of regular perturbances -- 6.2.5 Example -- 6.3 Singular perturbances -- 6.3.1 Singularly perturbed plant model -- 6.3.2 Fast motions in presence of singular perturbances -- 6.3.3 Selection of controller parameters -- 6.4 Nonsmooth nonlinearity in control loop -- 6.4.1 System preceded by nonsmooth nonlinearity -- 6.4.2 Describing function analysis of limit cycle in FMS -- 6.4.3 Effect of chattering on control accuracy -- 6.4.4 Example -- 6.5 Notes -- 6.6 Exercises -- Chapter 7 Realizability of desired output behavior -- 7.1 Control problem statement for MIMO control system -- 7.1.1 MIMO plant model -- 7.1.2 Control problem -- 7.2 Invertibility of dynamical systems -- 7.2.1 Role of invertibility of dynamical systems -- 7.2.2 Definition of invertibility of dynamic control system -- 7.2.3 Invertibility condition for nonlinear systems -- 7.3 Insensitivity condition for MIMO control system -- 7.3.1 Desired dynamics equations -- 7.3.2 Insensitivity condition -- 7.4 Internal stability -- 7.4.1 Boundedness of NID-control function -- 7.4.2 Concept of internal stability -- 7.4.3 Normal form of the plant model -- 7.4.4 Internal stability of linear systems -- 7.4.5 Internal stability of nonlinear systems -- 7.4.6 Degenerated motions and zero-dynamics -- 7.4.7 Example -- 7.5 Output regulation of SISO systems -- 7.5.1 Realizability of desired output behavior -- 7.5.2 Closed-loop system analysis -- 7.5.3 Example.

7.6 Switching regulator for boost DC-to-DC converter -- 7.6.1 Boost DC-to-DC converter circuit model -- 7.6.2 Model with continuous control variable -- 7.6.3 Switching regulator -- 7.6.4 External disturbance attenuation -- 7.7 Notes -- 7.8 Exercises -- Chapter 8 Design of MIMO continuous-time control systems -- 8.1 MIMO system without internal dynamics -- 8.1.1 MIMO system with identical relative degrees -- 8.1.2 MIMO system with different relative degrees -- 8.2 MIMO control system design (identical relative degrees) -- 8.2.1 Insensitivity condition -- 8.2.2 Control system with the relative highest derivatives in feedback -- 8.2.3 Fast-motion subsystem -- 8.2.4 Slow-motion subsystem -- 8.2.5 Control system design with zero steady-state error -- 8.2.6 Example -- 8.3 MIMO control system design (different relative degrees) -- 8.3.1 Insensitivity condition and control law structure -- 8.3.2 Closed-loop system analysis -- 8.3.3 Control accuracy -- 8.4 MIMO control system in presence of internal dynamics -- 8.4.1 Fast-motion subsystem -- 8.4.2 Slow-motion subsystem -- 8.4.3 Example -- 8.5 Decentralized output feedback controller -- 8.6 Notes -- 8.7 Exercises -- Chapter 9 Stabilization of internal dynamics -- 9.1 Zero placement by redundant control -- 9.2 Internal dynamics stabilization (particular case) -- 9.3 Internal dynamics stabilization (generalized case) -- 9.4 Stabilization of degenerated mode and zero dynamics -- 9.5 Methods of internal dynamics stabilization -- 9.6 Example -- 9.7 Notes -- 9.8 Exercises -- Chapter 10 Digital controller design based on pseudo-continuous approach -- 10.1 Continuous system preceded by zero-order hold -- 10.1.1 Control problem -- 10.1.2 Pseudo-continuous-time model with pure delay -- 10.2 Digital controller design -- 10.2.1 Insensitivity condition -- 10.2.2 Pseudo-continuous closed-loop system.

10.2.3 Influence of sampling period -- 10.2.4 Digital realization of continuous controller -- 10.2.5 Example -- 10.3 Digital controller design with compensation of delay -- 10.3.1 Control law structure -- 10.3.2 Closed-loop system analysis -- 10.3.3 Digital realization of continuous controller -- 10.3.4 Example -- 10.4 Notes -- 10.5 Exercises -- Chapter 11 Design of discrete-time control systems -- 11.1 SISO two-time-scale discrete-time control systems -- 11.1.1 Discrete-time systems -- 11.1.2 Control problem and insensitivity condition -- 11.1.3 Discrete-time control law -- 11.1.4 Two-time-scale motion analysis -- 11.1.5 Robustness of closed-loop system properties -- 11.1.6 Control accuracy -- 11.1.7 Example -- 11.2 SISO discrete-time control systems with small parameter -- 11.2.1 System with small parameter -- 11.2.2 Two-time-scale motion analysis -- 11.2.3 Interrelationship with fixed point theorem -- 11.2.4 Root placement of FMS characteristic polynomial -- 11.2.5 FMS design based on frequency-domain methods -- 11.3 MIMO two-time-scale discrete-time control systems -- 11.3.1 MIMO discrete-time systems -- 11.3.2 Control law -- 11.3.3 Two-time-scale motion analysis -- 11.3.4 Example -- 11.4 Notes -- 11.5 Exercises -- Chapter 12 Design of sampled-data control systems -- 12.1 SISO sampled-data control systems -- 12.1.1 Reduced order pulse transfer function -- 12.1.2 Input-output approximate model of linear system -- 12.1.3 Control law -- 12.1.4 Closed-loop system analysis -- 12.1.5 Selection of controller parameters -- 12.1.6 Nonlinear sampled-data systems -- 12.1.7 Example -- 12.2 MIMO sampled-data control systems -- 12.2.1 Control problem -- 12.2.2 MIMO continuous-time system preceded by ZOH -- 12.2.3 Control law -- 12.2.4 Fast-motion subsystem -- 12.2.5 Selection of controller parameters -- 12.2.6 Slow-motion subsystem -- 12.2.7 Example.

12.3 Notes.