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In robotics, in order to operate a humanoid robot, it is necessary to generate motions that have strictly dynamic consistency.
A good dynamic equivalence translation is the Contemporary English Version, although strictly dynamic equivalence translations are usually frowned on by serious scholars.
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In order to guarantee that a non-strictly dynamic output feedback with the gain matrices M, N, G and H designed for reduced-order subsystem (32) can stabilize system (30), the proposed method in this paper is considered.
For the strictly proper dynamic output feedback design of auxiliary system (20), a sufficient and necessary condition in terms of LMIs is given in the following theorem.
The design of a proper but not strictly proper dynamic output feedback controller is reduced to the simultaneous design of the static output feedback controller for the fast subsystem and the strictly proper dynamic output feedback controller for the auxiliary system, respectively.
We first show that a proper but not strictly proper dynamic output feedback controller designed for the reduced-order model generally is not a stabilizing compensator for the original system, even though the fast subsystem is stable.
In this paper, we focus on the problem of designing a proper but not strictly proper dynamic output feedback controller for a class of fast sampling discrete-time singularly perturbed systems using the reduced-order model.
Combining (19) and (20), we can see that the robustness problem considered here is to find some sufficient conditions such that the static output feedback gain matrix H and the strictly proper dynamic output feedback gain matrices M, N and G can assign the desired stable poles to the auxiliary systems and fast subsystem (5 - 6), respectively.
Given the initial condition (( x_{1}(0) xi (0) x_{2}(0) )^{T} = ( 1.5 1.5 1.5 )^{T}), the simulation results for the response of closed-loop system (5) are shown in Figures 1-2, from which it can be seen that the presented proper but not strictly proper dynamic output feedback control scheme can effectively guarantee the stability of the closed-loop system.
Next, we will investigate a non-strictly proper dynamic output feedback controller for system (1 - 2).
Strictly speaking, our dynamic liver scans only demonstrate that the performed parametrization of the AIF shape by an inverse power law and the stated value of the parameter b holds up to about 60 min p.i.. Beyond that time range, no direct proof for this specific (and invariant) shape exists.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com