Reset controllers are an example of nonlinear controllers that allow for extra design flexibility and they are motivated by the so called Clegg integrator introduced in 1958. This device is a particular type of a nonlinear integrator that operates in the same manner as the linear integrator whenever its input and output have the same sign and it resets its output to zero otherwise. Its describing function has the same magnitude plot as the linear integrator but it has a phase lag of only 38.1 degrees compared to the lag of 90 degrees for a linear integrator. This feature can be used to provide more flexibility in controller design. Indeed, it was recently shown that reset controllers may help remove some of the fundamental performance limitations of linear controllers. While these examples motivate the consideration of reset controllers, there are still no systematic methods for design of such systems.
Our results show that current models used to analyze reset systems are not appropriate (we use the example of the Clegg integrator to make this point). We propose a new class of models for reset systems that is more appropriate and show that by doing this we can obtain improvements in performance not achievable with the pre-existing models. We have developed Lyapunov like results that can be used to analyze general Lp stability properties of an important class of reset systems and presented results based on Linear Matrix Inequalities that can be used to construct appropriate piecewise quadratic Lyapunov functions. We believe that our results will lead to systematic methods for design of reset controllers.