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The switching condition of the controller is well defined.
The existence condition of the controller can be expressed by a convex optimization problem.
In [13] and Zhou [14], they studied the control problems of the semilinear equations by assuming (1), (3), a Lipschitz continuity of and a range condition of the controller with an inequality constraint.
In this paper, we no longer require the compact property in (1), the uniform boundedness in (2), and the inequality constraint on the range condition of the controller, but instead we need the regularity and a variation of solutions of the given equations.
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Then, we present the implications of these conditions on the controller design task focusing in stabilizations/destabilization of network processes under static negative feedback.
In the last section, we give a simple example to which the range conditions of the controller can be applied.
The stability of the designed controller is proven and sufficient conditions of the controller gains to stabilize the system are given.
The approach is flexible enough to allow designing a reduced-order controller for each subsystem with the same robustness condition of the centralized controller.
By combining the asynchronous switching, an improved stabilization approach is given, and existence conditions of the controllers associated with the corresponding ADT switching are formulated in terms of a set of linear matrix inequalities.
The adaptation is required because the stability condition of the feedback controller depends of the accuracy of one of the estimated non-linear maps.
The partitioning of a system model will condition the structure of the controller as well as its design.
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