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Third, we analyze the global motion of the robot under the controller and establish conditions on the control parameters that ensure attainment of the swing-up control objective; specifically, we determine the relationship between the closed-loop equilibrium points and a control parameter.
Third, this paper carries out a global analysis of the motion of the robot under the controller, and establishes some conditions on control parameters for achieving the swing-up control objective.
By (51) and (52), we have V i ( z i ( t ) ) ≤ ξ V i ( z i ( 0 ) ) e ( − 2 α δ + 2 t ω, ∀ t ≥ 0. On the other hand, using the condition (18), we have obtained the following: ∥ z i ( t ) ∥ ≤ N ξ γ e t ω, ∀ t ≥ 0. which implies the dynamical networks (7) is exponentially stable under the controller H2, then exponential synchronization of the controlled dynamical networks (5) is achieved.
His skill as an organiser and his sympathy with performers and composers led to his appointment as head of the music department, No 2 in the hierarchy under the controller – first Nicholas Kenyon, and later Roger Wright.
Proof Under the controller (4), the resulting closed-loop system can be written as (5).
The OFC maintains status information such as flow tables of all switches under the controller.
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Theorem 2. Isochronal function projective synchronization between Lorenz system (10) and delayed Lorenz system (9) will be realized under the controllers (11) and parameter updating laws (13).
Hence GFPS between the transmitter system (8) and the receiver system (9) is achieved and the uncertain parameter is also identified in the receiver end simultaneously under the controllers (14) and the parameter update rule (15).
Theorem 3. Isochronal function projective synchronization between hyper-chaotic Chen system (15) and delayed hyper-chaotic Chen system (14) will be achieved under the controllers (16) and parameter updating laws (18).
Since that is a complex model with the highly nonlinear multivariable strongly coupled and under-actuated property, the controller design of it was very difficult.
Under the control of super controller, there are x*y queuing models in HybridFlow.
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