Linear Systems Theory

Linear systems theory is the cornerstone of control theory and a well-established discipline that focuses on linear differential equations from the perspective of control and estimation. In this textbook, João Hespanha covers the key topics of the field in a unique lecture-style format, making the book easy to use for instructors and students. He looks at system representation, stability, controllability and state feedback, observability and state estimation, and realization theory. He provides the background for advanced modern control design techniques and feedback linearization, and examines advanced foundational topics such as multivariable poles and zeros, and LQG/LQR. The textbook presents only the most essential mathematical derivations, and places comments, discussion, and terminology in sidebars so that readers can follow the core material easily and without distraction. Annotated proofs with sidebars explain the techniques of proof construction, including contradiction, contraposition, cycles of implications to prove equivalence, and the difference between necessity and sufficiency. Annotated theoretical developments also use sidebars to discuss relevant commands available in MATLAB, allowing students to understand these important tools. The balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. Solutions to the theoretical and computational exercises are also available for instructors. Easy-to-use textbook in unique lecture-style format Sidebars explain topics in further detail Annotated proofs and discussions of MATLAB commands Balanced chapters can each be taught in two hours of course lecture Solutions to exercises available to instructors COVER......Page 1 TITLE......Page 4 COPYRIGHT......Page 5 CONTENTS......Page 8 PREAMBLE......Page 14 LINEAR SYSTEMS I - BASIC CONCEPTS......Page 18 I: SYSTEM REPRESENTATION......Page 20 1 STATE-SPACE LINEAR SYSTEMS......Page 22 2 LINEARIZATION......Page 28 3 CAUSALITY, TIME INVARIANCE, AND LINEARITY......Page 39 4 IMPULSE RESPONSE AND TRANSFER FUNCTION OF STATE-SPACE SYSTEMS......Page 48 5 SOLUTIONS TO LTV SYSTEMS......Page 58 6 SOLUTIONS TO LTI SYSTEMS......Page 63 7 SOLUTIONS TO LTI SYSTEMS: THE JORDAN NORMAL FORM......Page 72 II: STABILITY......Page 78 8 INTERNAL OR LYAPUNOV STABILITY......Page 80 9 INPUT-OUTPUT STABILITY......Page 97 10 PREVIEW OF OPTIMAL CONTROL......Page 104 III: CONTROLLABILITY AND STATE FEEDBACK......Page 110 11 CONTROLLABLE AND REACHABLE SUBSPACES......Page 112 12 CONTROLLABLE SYSTEMS......Page 127 13 CONTROLLABLE DECOMPOSITIONS......Page 135 14 STABILIZABILITY......Page 140 IV: OBSERVABILITY AND OUTPUT FEEDBACK......Page 150 15 OBSERVABILITY......Page 152 16 OUTPUT FEEDBACK......Page 165 17 MINIMAL REALIZATIONS......Page 174 LINEAR SYSTEMS II-ADVANCED MATERIAL......Page 182 V: POLES AND ZEROS OF MIMO SYSTEMS......Page 184 18 SMITH-MCMILLAN FORM......Page 186 19 STATE-SPACE ZEROS, MINIMALITY, AND SYSTEM INVERSES......Page 194 VI: LQR/LQG OPTIMAL CONTROL......Page 206 20 LINEAR QUADRATIC REGULATION (LQR)......Page 208 21 THE ALGEBRAIC RICCATI EQUATION (ARE)......Page 214 22 FREQUENCY DOMAIN AND ASYMPTOTIC PROPERTIES OF LQR......Page 221 23 OUTPUT FEEDBACK......Page 240 24 LQG/LQR AND THE Q PARAMETERIZATION......Page 255 25 Q DESIGN......Page 260 BIBLIOGRAPHY......Page 274 E......Page 276 L......Page 277 O......Page 278 S......Page 279 Z......Page 280