142 research outputs found
Sampled-Data Control for Singular Neutral System
This study is concerned with the ∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed ∞ performance. Then, the ∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective
H
This study is concerned with the H∞ control problem for singular neutral system based on sampled-data. By input delay approach and a composite state-derivative control law, the singular system is turned into a singular neutral system with time-varying delay. Less conservative result is derived for the resultant system by incorporating the delay decomposition technique, Wirtinger-based integral inequality, and an augmented Lyapunov-Krasovskii functional. Sufficient conditions are derived to guarantee that the resulting system is regular, impulse-free, and asymptotically stable with prescribed H∞ performance. Then, the H∞ sampled-data controller is designed by means of linear matrix inequalities. Finally, two simulation results have shown that the proposed method is effective
Stabilization of underactuated linear coupled reaction-diffusion PDEs via distributed or boundary actuation
This work concerns the exponential stabilization of underactuated linear
homogeneous systems of parabolic partial differential equations (PDEs) in
cascade (reaction-diffusion systems), where only the first state is controlled
either internally or from the right boundary and in which the diffusion
coefficients are distinct. For the distributed control case, a
proportional-type stabilizing control is given explicitly. After applying modal
decomposition, the stabilizing law is based on a transformation for the ODE
system corresponding to the comparatively unstable modes into a target one,
where the calculation of the stabilization law is independent of the
arbitrarily large number of these modes. This is achieved by solving
generalized Sylvester equations recursively. For the boundary control case, the
proposed controller is dynamic under appropriate sufficient conditions on the
coupling matrix (reaction term). A dynamic extension technique is first
performed via trigonometric change of variables that places the control
internally. Then, modal decomposition is applied followed by a state
transformation of the ODE system which must be stabilized in order to be
written in a form in which a dynamic law can be established. For both
distributed and boundary control systems, a constructive and scalable
stabilization algorithm is proposed, as the choice of the controller gains is
independent of the number of unstable modes and only relies on the
stabilization of the reaction term. The present approach solves the problem of
stabilization of underactuated systems when in the presence of distinct
diffusion coefficients. The problem is not directly solvable, similarly to the
scalar PDE case.Comment: arXiv admin note: substantial text overlap with arXiv:2202.0880
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