This paper introduces a subclass of positive systems involving input derivatives, which we formally define it as input derivative positive systems. Due to the presence of input derivatives, we provide an algebraic transformation to eliminate the derivative inputs to accommodate the process of stabilization by state feedback. This elimination transfers the input derivative in the output equation, which does not interfere with the design process. Stabilization of input derivative positive systems is performed through its equivalent transformed positive systems in standard form using LMI. To take advantage of this stabilization process, we utilize it for stabilization of positive singular systems. Consequently, we analyze singular systems and its equivalent transformations, which admit derivative input. Thus, algebraic transformation is employed to eliminate these derivative inputs. Finally, we establish the connection between stabilization of positive singular systems and stabilization of input derivative systems by a modified LMI. Numerical examples are included to support the theoretical result.

This paper considers the data-driven control problem for the important class of positive systems. Due to the fact that such systems appear in diverse application areas whereby data are collected for identification and control, they are qualified candidates for data-driven control. Using fundamental concept of persistently exciting data and formulas for data-driven control, we provide an initial attempt to solve the positive stabilization of linear systems by input-output data. The result is useful in the sense that no subspace identification is required to obtain system matrices. With the aid of available results of positive systems and recent development of data-driven analysis of dynamic system, we formulate and solve data-driven positive stabilization using data-dependent linear matrix inequalities. The structural constraint of positivity makes the task challenging. Nevertheless it is possible to use this framework for positive output feedback and robust optimal control problems as well.

This paper considers the design of an integrated observer structure termed as Proportional Integral Fading Unknown Input Observer (PIFUIO). The advantages of PIO and UIO observers are used in robust fault detection. The UIO decouples the unknown input disturbance while PIO allows to estimates the faults. It is shown that the fading term of this observer plays a distinct role in reliable estimation of faults decoupled from the unknown disturbance or vice versa. The robust detection of sensor fault is also considered with the presence of unknown inputs. Indirect and direct design procedures for sensor fault detection are provided. Numerical examples are included to illustrate the advantage of PIFUIO.