Description 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, Joao 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
Table of Contents Part II: SYSTEM REPRESENTATION
Chapter 1: STATE-SPACE LINEAR SYSTEMS
Chapter 2: LINEARIZATION
Chapter 3: CAUSALITY, TIME INVARIANCE, AND LINEARITY
Chapter 4: IMPULSE RESPONSE AND TRANSFER FUNCTION OF STATESPACE SYSTEMS
Chapter 5: SOLUTIONS TO LTV SYSTEMS
Chapter 6: SOLUTIONS TO LTI SYSTEMS
Chapter 7: SOLUTIONS TO LTI SYSTEMS: THE JORDAN NORMAL FORM
Part II: STABILITY
Chapter 8: INTERNAL OR LYAPUNOV STABILITY
Chapter 9: INPUT-OUTPUT STABILITY
Chapter 10: PREVIEW OF OPTIMAL CONTROL
Part III: CONTROLLABILITY AND STATE FEEDBACK
Chapter 11: CONTROLLABLE AND REACHABLE SUBSPACES
Chapter 12: CONTROLLABLE SYSTEMS
Chapter 13: CONTROLLABLE DECOMPOSITIONS
Chapter 14: STABILIZABILITY
Part IV: OBSERVABILITY AND OUTPUT FEEDBACK
Chapter 15: OBSERVABILITY
Chapter 16: OUTPUT FEEDBACK
Chapter 17: MINIMAL REALIZATIONS
Part V: POLES AND ZEROS OF MIMO SYSTEMS
Chapter 18: SMITH-MCMILLAN FORM
Chapter 19: STATE-SPACE ZEROS, MINIMALITY, AND SYSTEM INVERSES
Part VI: LQR/LQG OPTIMAL CONTROL
Chapter 20: LINEAR QUADRATIC REGULATION (LQR)
Chapter 21: THE ALGEBRAIC RICCATI EQUATION (ARE)
Chapter 22: FREQUENCY DOMAIN AND ASYMPTOTIC PROPERTIES OF LQR
Chapter 23: OUTPUT FEEDBACK
Chapter 24: LQG/LQR AND THE Q PARAMETERIZATION
Chapter 25: Q DESIGN
Joao P. Hespanha is professor of electrical engineering at the University of California, Santa Barbara, where he is associate director of the Center for Control, Dynamical Systems and Computation.