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The mechanical impedance of the human arm can be measured to quantitatively assess the motor function. In this paper, an adaptive least square estimation method is proposed for online measurement of the mechanical impedance of the arm, without force or acceleration sensors, which extremely reduces the expenses and complexity of rehabilitation robots. The proposed strategy may also be used for monitoring the dynamic changes of the mechanical impedance. Estimation of time-varying force is also the other capability of the algorithm. The closed-loop stability of the system is analytically shown using the Lyapunov stability theorem. To show the applications of the proposed scheme, two main scenarios are described which can be used for the rehabilitation robots to assess the motor recovery of the patients undergoing the rehabilitation sessions. To validate the scheme, a 2-DOF manipulator is adopted to illustrate the accuracy of the impedance and force estimations in noiseless and noisy conditions. [ABSTRACT FROM AUTHOR]

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities. [ABSTRACT FROM AUTHOR]

A new method is proposed in this article in order to determine a guaranteed interval of time delay in input signal for a class of non-linear control systems with state feedback. This method is based on the stability sufficient condition of a non-linear control system using the Lyapunov direct approach. For this purpose, the dynamic equations of the non-linear input-delayed system are reformulated as a non-linear system without delay, but with delay-dependent coefficients in the state-space description. The control strategy is considered a linear state feedback. Then, by introducing an appropriately related Lyapunov candidate, the stability sufficient condition of the closed-loop system is satisfied, leading to a guaranteed interval of delay according to the state feedback gain. The main results are gathered and proved as a lemma. The effectiveness of this proposed method is investigated by simulating the state feedback control of a non-linear synchronous generator with a delay in input. [ABSTRACT FROM AUTHOR]