Linear Control Systems: Structure, Stability, Optimality by Murat Arcak

This book develops linear control theory from first principles, building on the foundations of linear algebra. Vector spaces, inner products, eigenstructure, and the singular value decomposition (SVD) form the structural backbone of the presentation, yielding a mathematically self-contained and conceptually unified treatment of linear systems. Geometric interpretations clarify system structure, controllability, observability, stability, and balanced truncation. A central emphasis is optimal control, especially the linear quadratic regulator (LQR). The text avoids reliance on Laplace-transform machinery, introducing transfer functions in the spirit of Heaviside’s operational calculus and integrating them into a broader state-space narrative. Developed from lecture notes for EE 221A (Linear Systems) at the University of California, Berkeley, the book reflects years of pedagogical refinement.