State and output feedback stabilization for second-order nonholonomic chained systems based on sampled data control approach

This paper proposes new state and output feedback control systems based on sampled data control for a class of nonholonomic systems in second-order chained form. Our novel approach is to find a time-varying coordinate transformation by which the chained system discretized with the zero order hold and the sampler is transformed into a simple linear time-invariant discrete-time system. The contributions are as follows. Firstly, the problem of finding state feedback controllers to stabilize the chained systems is reduced to the well-known pole assignment problem for linear time-invariant discrete-time systems. As a result, a simple and explicit design method of the state feedback controller is obtained. Secondly, design problems of observers and dynamic output feedback controllers to stabilize the chained systems are posed and are solved. The problems are reduced to the well-known linear control problems. The proposed design methods are simple and straightforward.