| Preface | p. vii |
| Introduction | p. 1 |
| Notation | p. 1 |
| Acronyms | p. 3 |
| Basic ideas and motivations | p. 3 |
| The spirit of the book | p. 3 |
| Solving a problem | p. 5 |
| Conservative or intractable? | p. 6 |
| How to avoid reading this book | p. 8 |
| How to benefit from reading this book | p. 9 |
| Past work referencing | p. 9 |
| Outline of the book | p. 9 |
| The link with Lyapunov's theory | p. 10 |
| Uncertain systems | p. 13 |
| Constrained control | p. 18 |
| Required background | p. 25 |
| Related topics and reading | p. 26 |
| Lyapunov and Lyapunov-like functions | p. 27 |
| State space models | p. 27 |
| Differential inclusions | p. 29 |
| Model absorbing | p. 30 |
| The pitfall of equilibrium drift | p. 32 |
| Lyapunov derivative | p. 34 |
| Solution of a system of differential equations | p. 34 |
| The upper-right Dini derivative | p. 35 |
| Derivative along the solution of a differential equation | p. 36 |
| Special cases of directional derivatives | p. 37 |
| Lyapunov functions and stability | p. 39 |
| Global stability | p. 40 |
| Local stability and ultimate boundedness | p. 43 |
| Control Lyapunov Functions | p. 45 |
| Associating a control law with a Control Lyapunov Function: state feedback | p. 46 |
| Associating a control law with a Control Lyapunov Function: output feedback | p. 53 |
| Finding a Control Lyapunov Function | p. 54 |
| Polytopic systems | p. 54 |
| The convexity issue | p. 57 |
| Fake Control Lyapunov Functions | p. 57 |
| Lyapunov-like functions | p. 60 |
| Discrete-time systems | p. 62 |
| Converse Lyapunov theorems | p. 68 |
| Literature review | p. 69 |
| Exercises | p. 70 |
| Convex sets and their representation | p. 73 |
| Convex functions and sets | p. 73 |
| Operations between sets | p. 76 |
| Minkowski function | p. 79 |
| The normal and the tangent cones | p. 81 |
| Ellipsoidal sets | p. 83 |
| Polyhedral sets | p. 86 |
| Other families of convex sets | p. 94 |
| Exercises | p. 96 |
| Invariant sets | p. 99 |
| Basic definitions | p. 99 |
| Nagumo's theorem | p. 101 |
| Proof of Nagumo's theorem for practical sets and regular f | p. 104 |
| Generalizations of Nagumo's theorem | p. 106 |
| An example of application of Nagumo's theorem | p. 108 |
| Discrete-time systems | p. 110 |
| Positive invariance and fixed point theorem | p. 112 |
| Convex invariant sets and linear systems | p. 114 |
| Ellipsoidal invariant sets | p. 120 |
| Ellipsoidal invariant sets for continuous-time systems | p. 120 |
| Ellipsoidal invariant sets for discrete-time systems | p. 124 |
| Polyhedral invariant sets | p. 125 |
| Contractive polyhedral sets for continuous-time systems | p. 126 |
| Contractive sets for discrete-time systems | p. 135 |
| Associating a control with a polyhedral control Lyapunov function and smoothing | p. 138 |
| Existence of positively invariant polyhedral C-sets | p. 142 |
| The positive description | p. 143 |
| Other classes of invariant sets and historical notes | p. 144 |
| Exercises | p. 146 |
| Dynamic programming | p. 149 |
| Infinite-time reachability set | p. 149 |
| Linear systems with linear constraints | p. 156 |
| State in a tube: time-varying and periodic case | p. 164 |
| Historical notes and comments | p. 167 |
| Backward computation of Lyapunov functions | p. 168 |
| The largest controlled invariant set | p. 171 |
| The uncontrolled case: the largest invariant set | p. 179 |
| Comments on the results | p. 184 |
| Exercises | p. 188 |
| Set-theoretic analysis of dynamic systems | p. 191 |
| Set propagation | p. 191 |
| Reachable and controllable sets | p. 191 |
| Computation of set propagation under polytopic uncertainty | p. 194 |
| Propagation of uncertainties via ellipsoids | p. 197 |
| 0-Reachable sets with bounded inputs | p. 198 |
| Reachable sets with pointwise-bounded noise | p. 198 |
| Infinite-time reachability and l[subscript 1] norm | p. 207 |
| Reachable sets with energy-bounded noise | p. 209 |
| Historical notes and comments | p. 212 |
| Stability and convergence analysis of polytopic systems | p. 212 |
| Quadratic stability | p. 213 |
| Joint spectral radius | p. 213 |
| Polyhedral stability | p. 215 |
| The robust stability radius | p. 217 |
| Best transient estimate | p. 218 |
| Performance analysis of dynamical systems | p. 220 |
| Peak-to-peak norm evaluation | p. 221 |
| Step response evaluation | p. 226 |
| Impulse and frequency response evaluation | p. 228 |
| Norm evaluation via LMIs | p. 229 |
| Periodic system analysis | p. 231 |
| Exercises | p. 233 |
| Control of parameter-varying systems | p. 235 |
| Robust and gain-scheduling control | p. 237 |
| Stabilization of LPV systems via quadratic Lyapunov functions | p. 241 |
| Quadratic stability | p. 242 |
| Quadratic stabilizability | p. 242 |
| Quadratic Lyapunov functions: the discrete-time case | p. 244 |
| Quadratic stability and H[infinity] norm | p. 245 |
| Limits of quadratic functions and linear controllers | p. 246 |
| Notes about quadratic stabilizability | p. 251 |
| Polyhedral Lyapunov functions | p. 251 |
| Polyhedral stabilizability | p. 251 |
| Universality of polyhedral Lyapunov functions (and their drawbacks) | p. 256 |
| Smoothed Lyapunov functions | p. 261 |
| Gain-scheduling linear controllers and duality | p. 263 |
| Duality in a quadratic framework | p. 267 |
| Exercises | p. 268 |
| Control with time-domain constraints | p. 271 |
| Input constraints | p. 274 |
| Construction of a constrained control law and its associated domain of attraction | p. 278 |
| The stable-unstable decomposition | p. 283 |
| Systems with one or two unstable eigenvalues | p. 284 |
| Region with bounded complexity for constrained input control | p. 291 |
| Domain of attraction for input-saturated systems | p. 295 |
| State constraints | p. 299 |
| A case study | p. 301 |
| Assigning an invariant (and admissible) set | p. 306 |
| Control with rate constraints | p. 312 |
| The rate-bounding operator | p. 314 |
| Output feedback with constraints | p. 315 |
| The tracking problem | p. 317 |
| Reference management device | p. 319 |
| The tracking domain of attraction | p. 324 |
| Examples of tracking problems | p. 330 |
| Exercises | p. 333 |
| (Sub-)Optimal control | p. 337 |
| Minimum-time control | p. 337 |
| Worst-case controllability | p. 337 |
| Time optimal controllers for linear discrete-time systems | p. 341 |
| Time optimal controllers for uncertain systems | p. 342 |
| Optimal peak-to-peak disturbance rejection | p. 347 |
| Constrained receding-horizon control | p. 352 |
| Receding-horizon: the main idea | p. 352 |
| Recursive feasibility and stability | p. 355 |
| Receding horizon control in the presence of disturbances | p. 360 |
| Relatively optimal control | p. 365 |
| The linear dynamic solution | p. 369 |
| The nonlinear static solution | p. 377 |
| Exercises | p. 386 |
| Set-theoretic estimation | p. 389 |
| Worst-case estimation | p. 390 |
| Set membership estimation for linear systems with linear constraints | p. 396 |
| Approximate solutions | p. 403 |
| Bounding ellipsoids | p. 408 |
| Energy-bounded disturbances | p. 408 |
| Including observer errors in the control design | p. 410 |
| Literature review | p. 412 |
| Exercises | p. 412 |
| Related topics | p. 415 |
| Adaptive control | p. 415 |
| A surge control problem | p. 420 |
| The domain of attraction | p. 425 |
| Systems with constraints | p. 426 |
| Hybrid and switching systems | p. 430 |
| Switching and switched systems | p. 432 |
| Switching among controllers | p. 436 |
| Relay systems | p. 441 |
| Planar systems | p. 447 |
| Exercises | p. 449 |
| Appendix | p. 451 |
| Remarkable properties of the Euler auxiliary system | p. 451 |
| MAXIS-G: a software for the computation of invariant sets for constrained LPV systems | p. 456 |
| Software availability | p. 458 |
| Web addresses | p. 458 |
| References | p. 459 |
| Index | p. 477 |
| Table of Contents provided by Ingram. All Rights Reserved. |
