Analysis of input derivative dynamic systems and its stabilization by state feedback

Bahram Shafai, Fatemeh Zarei

Abstract: This paper considers the analysis of dynamic systems represented by state space models and general differential equations incorporating input derivatives. First, the connection between the class of systems with derivative inputs and singular systems is established. An elimination procedure for input derivatives is given, which transfers the derivative terms from the state equation to the output equation allowing stabilization by state feedback to be performed. Second, we consider the general differential equations with derivatives of inputs and outputs and derive an equivalent state space description in standard form, which incorporates the derivatives in the state variables. This is essential since a suitable feedback configuration should involve both input and output as well as their derivatives. We provide an appropriate state space model that allows stabilization by state feedback controller to be performed. Finally, a subclass of positive system involving input derivatives is considered as a special case. It is shown that stabilization of input derivative positive system can be achieved through its equivalent positive system in standard form using LMI. Numerical examples are included to support the theoretical results.