This paper proposes a notion of a controllability measure of discrete-time piecewise affine systems, which is a natural extension of the controllability gramian of linear systems. Although this measure is calculated in a probabilistic way, it may be applied to control of biological systems for providing a policy to experiments for pharmaceutical developments. Thus an application to gene regulatory control of luminescence in the marine bacterium modeled by the piecewise affine system is discussed in this paper.

This paper proposes a robust fuzzy integral controller for output regulating a class of affine nonlinear systems subject to a bias reference to the origin. First, a common biased fuzzy model is introduced for a class of continuous/discrete-time affine nonlinear systems, such as dc-dc converters, robotic systems. Then, combining an integrator and parallel distributed compensators, the fuzzy integral regulator achieves an asymptotic regulation. Moreover, when considering disturbances or unstructured certainties, a virtual reference model is presented and provides a robust gain design via LMI techniques. In this case, H∞ performances is guaranteed. Note that the information regarding the operational point and bias terms are not required during the controller implementation. Thus, the controller can be applied to a multi-task regulation. Finally, three numerical simulations show the expected results.