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This article aims to design proportional-derivative (PD) controllers for interval positive linear systems in the continuous-time domain, which still remains a widely-discussed open problem in positive systems theory. The specific objective is to design a PD controller for the system with interval uncertain parameters and time-varying delay, which simultaneously ensures closed-loop system stability and preserves positivity. The work proposes a systematic framework, with the aim of finding PD controller gains for positive robust stabilization. The methodology and algorithm are presented first in the study, and the performance of such methods is instantiated by numerical examples. [ABSTRACT FROM AUTHOR]

• An unknown input FE filter was proposed to simultaneously estimate system states, actuator faults and sensor faults. • An FE filter-based integral sliding mode FTC scheme was developed, it is shown that the trajectory of the original system converges to zero. • This study proposed the finite frequency FE and FTC methods, so that the effects of time-delays and Lipschitz function can be tackled. • The designed approach has less conservativeness than those full frequency design techniques in Lan and Patton [5] , Qi and Ma [22]. This work describes an integrated fault estimation (FE) and fault tolerant control (FTC) strategy for a class of uncertain Lipschitz systems subject to time-delays in finite frequency domain. First, an FE filter is constructed by modeling the actuator faults and sensor faults as parameter changes. Second, an integral-type sliding mode FTC law based on the FE filter is developed, such that all states of the closed-loop system converge to the origin. By using the reconstructed Lipschitz property, the filter error system and the controlled system are rewritten as an augmented linear parameter varying (LPV) system. In addition, sufficient conditions for the augmented LPV system to have one full frequency and two finite frequency H ∞ index bounds are converted to linear matrix inequalities. Finally, two examples are delivered to demonstrate the validity and benefits of the proposed method. [ABSTRACT FROM AUTHOR]