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A note on the Lyapunov matrix equation
IEEE Transactions on Automatic Control, 1981In [5] bound for the determinant of the solution to the Lyapunov matrix equation was reported. This note gives an another bound for this value.
N Fukuma
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On the Lyapunov matrix differential equation
IEEE Transactions on Automatic Control, 1986A lower bound for the determinant of the solution to the Lyapunov matrix differential equation is derived. It is shown that this bound is obtained as a solution to a simple scalar differential equation. In the limiting case where the solution to the Lyapunov differential equation becomes stationary, the result reduces to one of the existing bounds for ...
N Fukuma
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An explicit solution to the generalized Lyapunov matrix inequality
Systems & Control LetterszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mario Spirito, Daniele Astolfi
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Comments on "On the Lyapunov matrix equation"
IEEE Transactions on Automatic Control, 1975The 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, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bhaskar Dubey, Raju K. George
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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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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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On bounds of Lyapunov's matrix equation
IEEE Transactions on Automatic Control, 1979In this paper, new bounds are given for the matrix solution of the Lyapunov equation A'P+ PA+Q=0 . It is shown that it is always possible to achieve a lower bound, while the upper bound can be obtained for a specified class of Q matrices which is given. The results are compared to those given in [1] through some examples.
Geromel, J. C., Bernussou, J.
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On the Lyapunov matrix equation
IEEE Transactions on Automatic Control, 1974Given the Lyapunov matrix equation A'Q + QA = -P a fundamental inequality which is satisfied by the extremal eigenvalues of the matrices Q and P , provided A is a stability matrix, is established. This result, besides being interesting from a theoretical standpoint, is extremely useful in the determination of suboptimal controllers for the minimum time
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On the Lyapunov matrix equation
IEEE Transactions on Automatic Control, 1980In this paper the inequality which is satisfied by the determinant of the solution of the Lyapunov matrix equation A'Q + QA = - D is presented. The result makes possible a lower estimate of product eigenvalues of the matrix Q and dependence from eigenvalues of the matrices A and D .
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