Using the variable substitution method, state space differential equations of the structure are established.
Firstly, by constructing a proper variable substitution,the original system is transformed into the first order differential system.
A variable substitution method is proposed to obtain the apparently-uncoupled mathematical model of the rigid flexible liquid spacecraft.
A novel static output-feedback design method based on the variable substitution is employed in the controller design.
A variable substitution method, in which the main branch of logarithmic function is chosen, is proposed to solve this problem.
The solution methods include variable substitution, perturbation technique, Laplace transformation, Sturm-Liouville eigenvalue theory, orthogonal transformation and numerical inversion.
The reduced order model, which is used to design the closed-loop control system, is obtained by the combination of modal expansion and variable substitution.
State-space formulations are developed based on the exact elasticity equations, and in particular, a variable substitution technique is used to derive the state equations with constant coefficients.
First of all, the generalized variable substitution controller is designed to establish the master slave finite-time synchronization scheme for the Lorenz Stenflo systems.
First, by choosing a proper variable substitution, inertial memristive neural networks described by second-order differential equations can be transformed into first-order differential equations.
Applying this criterion, some sufficient finite-time synchronization criteria under various generalized variable substitution controllers are further derived in the algebraic form.
