Advanced Mathematical Tools for Control Engineers: Volume 1: Deterministic SystemsAdvanced Mathematical Tools for Control Engineers: Volume 1 provides a blend of Matrix and Linear Algebra Theory, Analysis, Differential Equations, Optimization, Optimal and Robust Control. It contains an advanced mathematical tool which serves as a fundamental basis for both instructors and students who study or actively work in Modern Automatic Control or in its applications. It is includes proofs of all theorems and contains many examples with solutions. It is written for researchers, engineers, and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to System and Automatic Control Theories.

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asymptotic Banach space bounded bounded variation called Cayley–Hamilton theorem compact completes the proof complex number continuous function contradiction converges convex convex function Corollary corresponding criterion defined denoted derivative eigenvalues eigenvector elements equivalently Example exists finite following inequality follows directly function f given Hankel operator hence Hermitian holds identity implies integral interval Laplace transformation Lebesgue Lebesgue integral Lemma Lemma is proven Lyapunov matrix matrix norm metric space minimal monotone nCO nonlinear nonnegative nonsingular norm obtain open set operator optimal control orthogonal pair polynomial problem Proposition pseudoinverse quadratic real numbers Remark result Riccati Riccati equation righthand side Rn×n satisfies sequence stable subset subspace Suppose symmetric Theorem is proven transformation vector zero