## Linear Control Systems: With solved problems and MATLAB examplesAnyone seeking a gentle introduction to the methods of modern control theory and engineering, written at the level of a first-year graduate course, should consider this book seriously. It contains: - A generous historical overview of automatic control, from Ancient Greece to the 1970s, when this discipline matured into an essential field for electrical, mechanical, aerospace, chemical, and biomedical engineers, as well as mathematicians, and more recently, computer scientists;
- A balanced presentation of the relevant theory: the main state-space methods for description, analysis, and design of linear control systems are derived, without overwhelming theoretical arguments;
- Over 250 solved and exercise problems for both continuous- and discrete-time systems, often including MATLAB simulations; and
- Appendixes on MATLAB, advanced matrix theory, and the history of mathematical tools such as differential calculus, transform methods, and linear algebra.
Another noteworthy feature is the frequent use of an inverted pendulum on a cart to illustrate the most important concepts of automatic control, such as: - Linearization and discretization;
- Stability, controllability, and observability;
- State feedback, controller design, and optimal control; and
- Observer design, reduced order observers, and Kalman filtering.
Most of the problems are given with solutions or MATLAB simulations. Whether the book is used as a textbook or as a self-study guide, the knowledge gained from it will be an excellent platform for students and practising engineers to explore further the recent developments and applications of control theory. |

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### Contents

Historical overview of automatic control | 3 |

11 Automatic control before the 1930s | 5 |

12 Classical period of automatic control | 12 |

13 Beginnings of modern control theory | 18 |

Modern control theory | 23 |

21 Statespace representation | 25 |

22 System properties | 34 |

23 State feedback and optimal control | 62 |

46 Stability | 239 |

47 Controllability and observability | 244 |

48 Canonical realizations | 251 |

49 State feedback | 255 |

410 Optimal control | 259 |

411 State observers | 263 |

412 Kalman filter | 265 |

413 Reducedorder observers | 272 |

24 State observers and estimators | 68 |

Part II Solved problems | 71 |

Continuous linear systems | 73 |

31 Simple differential equations | 75 |

32 Matrix theory | 83 |

33 Systems of linear differential equations | 95 |

34 Inputoutput representation | 98 |

35 Statespace representation | 113 |

36 Stability | 128 |

37 Controllability and observability | 134 |

38 Canonical realizations | 152 |

39 State feedback | 166 |

310 Optimal control | 178 |

311 State observers | 186 |

312 KalmanBucy filter | 194 |

313 Reducedorder observers | 199 |

Discrete linear systems | 207 |

41 Simple difference equations | 209 |

42 More matrix theory | 217 |

43 Systems of linear difference equations | 220 |

44 Inputoutput representation | 222 |

45 Statespace representation | 235 |

Exercise problems | 273 |

Part III Appendixes | 287 |

A quick introduction to MATLAB | 289 |

A2 Basic matrix operations | 290 |

A3 Plotting graphs | 294 |

A4 Data analysis | 295 |

A5 Data management and IO operations | 296 |

Mathematical preliminaries | 305 |

B2 Differential and difference equations | 306 |

B3 Laplace and ztransforms | 312 |

B4 Matrices and determinants | 318 |

Results from advanced matrix theory | 323 |

C2 Diagonal and Jordan forms | 328 |

C3 Similarity of matrices | 332 |

C4 Symmetric and Hermitian matrices | 338 |

C5 Quadratic forms and definiteness | 343 |

C6 Some special matrices | 351 |

C7 Rank pseudoinverses SVD and norms | 353 |

C8 Problems | 363 |

Bibliography | 369 |

373 | |

### Other editions - View all

Linear Control Systems: With solved problems and MATLAB examples Branislav Kisačanin,Gyan C. Agarwal No preview available - 2012 |

### Common terms and phrases

applied assume asymptotically stable Ax(t Bass-Gura formula BIBO stability calculate characteristic equation characteristic polynomial closed-loop system coefficients companion matrix complex Consider continuous-time system control theory controllability and observability controllability matrix controller form controller realization defined derive det(A det(C det(s determine diagonal difference equations differential equations discrete-time systems distinct eigenvalues eigenvalues eigenvectors corresponding estimation example Figure frequency hence Hermitian impulse response initial conditions input inverted pendulum Kalman filter Laplace transform linear systems Lyapunov equation Lyapunov stability MATLAB MATLAB command n x n negative noise nonsingular notation Note Nyquist observer form optimal control origin output plot poles positive definite symmetric positive semi-definite Problem Proof properties prove quadratic form real symmetric realization of H(s recursion result Riccati equation Section sense of Lyapunov similarity transformation Solution solve symmetric matrix system given system is controllable theorem transfer function u[fc unstable write xdot ylabel z-transform zero