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This book provides solutions to many engineering and mathematical problems related to the Lyapunov matrix equation. Geared toward an audience of engineers, applied mathematicians, computer scientists, and graduate students, it explores issues of mathematical development and applications, making it equally practical for problem solving and research. Its comprehensive treatment features self-contained chapters for quick and precise reference.
The authors offer a wide variety of techniques for solving and analyzing the algebraic, differential, and difference Lyapunov matrix equations of continuous-time and discrete-time systems. The matrix equations are considered in terms of three main categories: explicit solutions; approximate solutions characterized by different bounds, such as eigenvalue bounds, trace bounds, determinant bounds, and solution bounds; and numerical solutions suitable for computer calculations. Numerous examples of real-world systems appear throughout, illustrating the effectiveness of cited methods and algorithms.