The published literature for stability analysis of linear time-delay systems has attracted much interest among the researchers over the last five decades. In general, the stability for linear time-delay systems can be checked exactly only by eigenvalue considerations. Two types of stability conditions are delay-independent type, mainly used for arbitrarily large delays, and delay-dependent type, which is mostly useful in applications that consider maximum delay. In this paper, we consider a linear time-invariant system with delay differential equation form for quiet-standing case study as a derivative feedback control. When it is reasonably chosen with intentional delays, the effects of time delay for ankle torque can be used to improve and stabilize the response of the close-loop systems.
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