Linear Systems Theory : Second Edition

**A fully updated textbook on 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. This updated second edition of __Linear Systems Theory__ covers the subject's key topics in a unique lecture-style format, making the book easy to use for instructors and students. João Hespanha 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 tools. This second edition contains a large number of new practice exercises with solutions. Based on typical problems, these exercises guide students to succinct and precise answers, helping to clarify issues and consolidate knowledge. The book's balanced chapters can each be covered in approximately two hours of lecture time, simplifying course planning and student review. * 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 * New practice exercises with solutions included Contents Preamble Linear systems i — basic concepts Part I. System representation State-space linear systems Linearization Causality, time invariance, and linearity Impulse response and transfer function of state-space systems Solutions to LTV systems Solutions to LTI systems Solutions to LTI systems: the Jordan normal form Part II. Stability Internal or Lyapunov stability Input-output stability Preview of optimal control Part III Controllability and state feedback Controllable and reachable subspaces Controllable systems Controllable decompositions Stabilizability Part IV. Observability and output feedback Observability Output feedback Minimal realizations Linear systems II — advanced material Part V. Poles and zeros of Mimo systems Smith-McMillan form State-space poles, zeros, and minimality System inverses Part VI. LQR/LQG optimal control Linear Quadratic Regulation (LQR) The algebraic Riccati Equation (ARE) Frequency domain and asymptotic properties of LQR Output feedback LQG/LQR and the Q parameterization Q design Bibliography Index