The Lyapunov and Riccati equations are two of the fundamental equations of control and system theory, having special relevance for system identification, optimization, boundary value problems, power systems, signal processing, and communications. This study covers mathematical developments and applications while providing quick and easy references for solutions to engineering and mathematical problems. Examples of real-world systems are given throughout the text in order to demonstrate the effectiveness of the presented methods and algorithms. It should appeal to practicing engineers, theoreticians, applied mathematicians, and graduate students who seek a comprehensive view of the main results of the Lyapunov matrix equation. The text includes: techniques for solving and analysing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems; summaries and references at the end of each chapter; examples of the use of the equation to solve real-world problems; and quick and easy references for the solutions to engineering and mathematical problems using the Lyapunov equation.
