One application of Lyapunov’s matrix equation
Copyright policy )One application of Lyapunov’s matrix equation
On the basis of the matrix Lyapunov equation, the property of having fixed sign for an associated quadratic form in the space \(R^{n}\) or in some octant of this space is investigated. A theorem establishing this property is formulated and proved. Also, another theorem determines the conditions which guarantee the property of having fixed sign for the quadratic form. As an example, the stability of a system of four first order differential equations is considered.
Asymptotic stability in control theory, matrix Lyapunov equation, Linear systems in control theory, Lyapunov and storage functions, Matrix equations and identities, Algebraic theory of quadratic forms; Witt groups and rings, stability, quadratic form, property of having fixed sign
Asymptotic stability in control theory, matrix Lyapunov equation, Linear systems in control theory, Lyapunov and storage functions, Matrix equations and identities, Algebraic theory of quadratic forms; Witt groups and rings, stability, quadratic form, property of having fixed sign
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