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Comments on "On the Lyapunov matrix equation"

IEEE Transactions on Automatic Control, 1975
The Lyapunov matrix equation A'Q + QA = - P is considered in the above paper, where two fundamental inequalities are derived which are satisfied by the extremal eigenvalues of the matrices Q and P provided A is a stability matrix. Similar results are derived by an alternate more simple and straightforward approach using matrix norms.
Montemayor, J. J., Womack, Baxter F.
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Controllability of impulsive matrix Lyapunov systems

Applied Mathematics and Computation, 2015
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Dubey, Bhaskar, George, Raju K.
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The Lyapunov matrix-function

Nonlinear Analysis: Theory, Methods & Applications, 1984
For a system of equations \(dx/dt=f(x)\), \(f(0)=0\) where \(x\in R^ n\), \(f:N\to R^ n\), \(N\subset R^ n\) the author introduces the Lyapunov matrix-function (1) \({\mathcal B}(x)=\{w_{ij}(x)\}^ m_{i,j=1}\), \(w_{ij}(0)=0\); \(\bar {\mathcal B}(x)=\max_{i,j}w_{ij}(x)\), i,\(j\in [1,m]\) and its derivative \(\quad (2)\quad\overset \circ {\mathcal B}(x)
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