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Second, under the assumption, the output matrices of nonlinear switched system are with some special forms which can also be dealt by orthogonal procedure if they are not satisfied, multiple reduced-order switched observers are proposed by coordinate transformation approach such that the state estimation purpose is reached for original nonlinear switched systems.
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The method is conducted by investigating the open-loop steady-state multiplicity behaviour and the singularity of the process gain matrix of nonlinear systems simultaneously.
This method results in a canonical analysis of the matrix of nonlinear selection gradients.
Both membership functions and parametric matrices of considered nonlinear systems contain uncertain parameters.
Here, the CKF was used to solve the nonlinear issue while the VCE method was used for the noise covariance matrix of the nonlinear system real-time estimation.
It is proved that optimal state feedback gain matrix obtained from the LTV approximations converges to the optimal state feedback gain matrix of the nonlinear system.
One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed.
In the above discussion, we only focus on the parameter perturbations which are allowed in the stoichiometric matrix of the nonlinear model and environment.
The matrix of the nonlinear transformation that maps the MR study onto the MNI space was estimated by means of the SPM12 segment function and used to map tissue probabilistic atlases to the subject with the SPM12 inverse deformations utility.
As the time advances by the time integration, since the system matrix is the function of nonlinear modal stiffness matrix, the system matrix also is modified after each iteration within each time step.
The obtained criteria are in terms of linear matrix inequalities without transcendental equation, instead of nonlinear matrix inequalities, which reduces the computational burden.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com