Linear Systems

"There are three words that characterize this work: thoroughness, completeness and clarity. The authors are congratulated for taking the time to write an excellent linear systems textbook! ...The authors have used their mastery of the subject to produce a textbook that very effectively presents the theory of linear systems as it has evolved over the last thirty years. The result is a comprehensive, complete and clear exposition that serves as an excellent foundation for more advanced topics in system theory and control." —IEEE Transactions on Automatic Control "In assessing the present book as a potential textbook for our first graduate linear systems course, I find...[that] Antsaklis and Michel have contributed an expertly written and high quality textbook to the field and are to be congratulated.... Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference." —Automatica Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook. The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systems and control. Linear Systems is written as a textbook for a challenging one-semester graduate course; a solutions manual is available to instructors upon adoption of the text. The book’s flexible coverage and self-contained presentation also make it an excellent reference guide or self-study manual. ******* For a treatment of linear systems that focuses primarily on the time-invariant case using streamlined presentation of the material with less formal and more intuitive proofs, see the authors’ companion book entitled A Linear Systems Primer. Cover......Page 1 Linear Systems......Page 2 Copyright - ISBN: 0817644342......Page 3 Contents......Page 8 Preface......Page 14 1 Mathematical Descriptions of Systems......Page 18 1.1 Introduction......Page 19 1.2 Preliminaries......Page 25 1.3 Initial-Value Problems......Page 27 1.4 Examples of Initial-Value Problems......Page 30 *1.5 More Mathematical Preliminaries......Page 34 *1.6 Existence of Solutions of Initial-Value Problems......Page 38 *1.7 Continuation of Solutions......Page 43 *1.8 Uniqueness of Solutions......Page 46 *1.9 Continuous Dependence of Solutions on Initial Conditions and Parameters......Page 50 1.10 Systems of First-Order Ordinary Differential Equations......Page 54 1.11 Systems of Linear First-Order Ordinary Differential Equations......Page 64 1.12 Linear Systems: Existence, Uniqueness, Continuation, and Continuity witli Respect to Parameters of Solutions......Page 71 1.13 Solutions of Linear State Equations......Page 72 1.14 State-Space Description of Continuous-Time Systems......Page 75 1.15 State-Space Description of Discrete-Time Systems......Page 77 1.16 Input-Output Description of Systems......Page 82 1.17 Summary......Page 96 1.19 References......Page 97 1.20 Exercises......Page 98 2.1 Introduction......Page 111 2.2 Background Material......Page 113 2.3 Linear Homogeneous and Nonhomogeneous Equations......Page 155 2.4 Linear Systems with Constant Coefficients......Page 165 *2.5 Linear Periodic Systems......Page 178 2.6 State Equation and Input-Output Description of Continuous-Time Systems......Page 182 2.7 State Equation and Input-Output Description of Discrete-Time Systems......Page 191 2.8 An Important Comment on Notation......Page 207 2.10 Notes......Page 208 2.11 References......Page 209 2.12 Exercises......Page 210 3 Controllability, Observability, and Special Forms......Page 231 3.1 Introduction......Page 232 3.2 Reachability and Controllability......Page 243 3.3 Observability and Constructibility......Page 264 3.4 Special Forms......Page 280 *3.5 Poles and Zeros......Page 315 3.6 Summary......Page 325 3.7 Notes......Page 327 3.9 Exercises......Page 328 4 State Feedback and State Observers......Page 338 4.1 Introduction......Page 339 4.2 Linear State Feedback......Page 343 4.3 Linear State Observers......Page 367 4.4 Observer-Based Dynamic Controllers......Page 380 4.6 Notes......Page 387 4.7 References......Page 388 4.8 Exercises......Page 389 5 Realization Theory and Algorithms......Page 400 5.1 Introduction......Page 401 5.2 State-Space Realizations of External Descriptions......Page 402 5.3 Existence and Minimality of Realizations......Page 406 5.4 Realization Algorithms......Page 419 5.6 Notes......Page 441 5.8 Exercises......Page 442 6.1 Introduction......Page 449 6.2 Mathematical Background Material......Page 451 6.3 The Concept of an Equilibrium......Page 462 6.4 Qualitative Characterizations of an Equilibrium......Page 464 6.5 Lyapunov Stability of Linear Systems......Page 469 6.6 Some Geometric and Algebraic Stability Criteria......Page 478 6.7 The Matrix Lyapunov Equation......Page 485 6.8 Linearization......Page 494 6.9 Input-Output Stability......Page 498 6.10 Discrete-Time Systems......Page 506 6.11 Summary......Page 525 6.12 Notes......Page 526 6.13 References......Page 527 6.14 Exercises......Page 528 7 Polynomial Matrix Descriptions and Matrix Fractional Descriptions of Systems......Page 534 7.1 Introduction......Page 535 7.2 Background Material on Polynomial Matrices......Page 541 7.3 Systems Represented by Polynomial Matrix Descriptions......Page 570 7.4 Feedback Control Systems......Page 606 7.5 Summary......Page 651 7.6 Notes......Page 652 7.7 References......Page 653 7.8 Exercises......Page 655 A.1 Introduction......Page 662 A.2 Solving Linear Algebraic Equations......Page 663 A.3 Singular Values and Singular Value Decomposition......Page 665 A.4 Solving Polynomial and Rational Matrix Equations Using Interpolation Methods......Page 670 A.5 References......Page 676 Index......Page 678 '...A comprehensive, complete and clear exposition that serves as an excellent foundation for more advanced topics in system theory and control.'- IEEE Transactions on Automatic Control'[The authors] have contributed an expertly written and high quality textbook...and are to be congratulated.... Because of its mathematical sophistication and completeness the present book is highly recommended for use, both as a textbook as well as a reference.'- Automatica Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook. The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systems and control. Linear Systems is written as a textbook for a challenging one-semester graduate course; a solutions manual is available to instructors upon adoption of the text. The book's flexible coverage and self-contained presentation also make it an excellent reference guide or self-study manual. For a treatment of linear systems that focuses primarily on the time-invariant case using streamlined presentation of the material with less formal and more intuitive proofs, see the authors'companion book entitled A Linear Systems Primer.