In this paper we present a general linear matrix inequality-based analysis method to determine the performance of a SISO reset control system in both the L 2 gain and H 2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the L 2 gain performance and the H 2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear-based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed L 2 gain and H 2 norm calculations and show that, for an input constrained H 2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. of the controller states when the switching surface is reached. The rationale behind reset control can best be understood when considering an integrating controller in particular. An integrator 'sums' the error over time in order to achieve a zero steady-state error. However, when the error becomes zero for the first time, the integrator still has the 'summed' error stored in its states, and the subsequent 'emptying' of the integrator causes the error signal to overshoot. To reduce the overshoot, it might be beneficial to reset the state of this integrator to zero as soon as its input (the error) becomes zero. In this way the integrator state, containing the 'summed' error, is emptied instantaneously, and hence the overshoot is avoided. This concept was indeed validated by simulations in recent publications [5,6], showing a significant decrease of overshoot in the step response.The concept of reset control was first introduced in 1958 by means of the resetting integrator of Clegg [7]. The describing function of the Clegg integrator has

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Optical incremental encoders are extensively used for position measurements in motion systems. The position measurements suffer from quantization errors. Velocity and acceleration estimations obtained by numerical differentiation largely amplify the quantization errors. In this paper, the time stamping concept is used to obtain more accurate position, velocity and acceleration estimations. Time stamping makes use of stored events, consisting of the encoder counts and their time instants, captured at a high resolution clock. Encoder imperfections and the limited resolution of the capturing rate of the encoder events result in errors in the estimations. In this paper, we propose a method to extend the observation interval of the stored encoder events using a skip operation. Experiments on a motion system show that the velocity estimation is improved by 54% and the acceleration estimation by 92%.

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