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With resorting to a matrix transformation technique to separate Lyapunov variables from system matrices, sufficient conditions are established in terms of linear matrix inequalities (LMIs).
The modal expansion method and a matrix transformation technique are used to solve the system equations to obtain the natural frequencies and modes of system.
In contrast, if a given disturbed BN is not globally robust stable w.r.t. a fixed point or w.r.t. a limit cycle, system can achieve stability by a matrix transformation technique.
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Further, by using matrix transformation techniques, we show that the desired controller parameters can be obtained by solving a convex optimization problem involving linear matrix inequalities (LMIs).
The restraint matrices are integrated in to spline stiffness matrices using transformation technique to extract pure modes corresponding to local, distortional and global modes.
Using the transformation technique, the transformed model can be derived.
The proposed approach allows a pentadiagonal banded matrix system to be split into quasi-disjoint subsystems by using a linear algebraic transformation technique.
Based on a suitable Lyapunov Krasovskii functional, model transformation technique and Wirtinger-based double integral inequality, the general framework is obtained in terms of linear matrix inequalities to determine the finite time stability and to achieve the control design.
Another notion we need is that of matrix transformation.
For this purpose, we use the unitary transformation technique.
One of them is the Riccati transformation technique.
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