A piecewise-affine approach to observer design for a class of nonlinear systems linear in the input with a sampled output

This paper addresses the design of continuous-time piecewise-affine (PWA) observers for a class of nonlinear systems with sampled output. Building on observer theory for PWA systems, sufficient conditions are proposed such that a continuous-time PWA observer can be used to estimate the states of a nonlinear system linear in the input with sampled output yielding a convergent state estimation error. The method for observer design is a convex optimization approach in terms of linear matrix inequalities (LMIs). It is shown that the state estimation error, which is ultimately bounded, converges to a region and the size of the region depends on the sampling time and the PWA approximation error. The size of the region decreases as the sampling time and/or the PWA approximation error decrease. Results independent of the sampling time and dependent on the sampling time are provided. An example in robotics shows the effectiveness of the proposed approach.