Volume 4 • Issue 2 • PP: 19–25 • 2024
On the Nature of Solutions of Discrete Time Lyapunov Equations
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© 2024 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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This paper provides a method to solve the discrete time Lyapunov equation. Identified and discussed. If the equation takes the following form:
D (λy+μz) = λDy+ μDz , 𝑦,z∈ y; λ ,μ ∈𝐹 .
If ∃ a constant e∈∞ ∋ ||Dy|| ≤ e ||y||, y ∀Y. and D is bounded, then D is called a linear operator equation. In particular, (Lyapunov and Sylvester operator equations) are very important in differential equations, integral equations and many other branches of mathematics. The study of solutions and of the above equestion We also discussed operator equations and special kinds of operators and studied some elementary operators. These operators are generalizations of operators τ𝐴𝐷:𝐷(𝐻)→𝐷(𝐻) τ𝐴𝐷:𝜏𝐴𝐷(𝑦)=𝐴𝑦−𝑦𝐷, 𝑦∈𝐷(𝐻)
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References
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