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The obtained SMC ensures that the state trajectories reach the sliding surface in finite time and remain on it thereafter.
A controller is designed such that system trajectories reach sliding surface in finite time and remain there for all subsequent time.
Furthermore, variable structure controllers are developed to drive the state of the switched system to reach the single sliding surface in finite time and remain on it thereafter.
In addition, an appropriate sliding mode controller is designed to drive the state trajectories of error system to the prescribed sliding surface in finite time and remain on it evermore.
Secondly, static and dynamic output feedback variable structure controllers are designed that can drive the state of the switched system to reach the common sliding surface in finite time and remain them thereafter.
The control law can be tuned to force closed-loop trajectories to enter in some a priori fixed neighborhood of the origin in a finite time and remain thereafter.
"Time remaining: 3 hours".
Many dynamical systems are characterized by the property of possessing a bounded absorbing set where all trajectories enter in a finite time and thereafter remain inside.
A dissipative dynamical system is characterized by possessing a bounded absorbing set that all trajectories enter in a finite time and thereafter remain inside [1].
The control algorithms asymptotically stabilize the system with finite-time convergences, remaining robust amid disturbances and parametric uncertainties.
If there exists initial data that u blows up at finite time T, while v remain bounded up to that time, from Theorem 1.2 we have (1.5) holds, which is a contradiction.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com