H<inf>2</inf> gain scheduled observer based controllers for rational LPV systems

Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

“…The controller is applied to two-link robotic manipulator. Natural two-link robotic manipulator model has not any singular matrices, but it and similar mechanical systems can be converted to singular form by LPV conversion methods as in [22,36,37], which is not in the focus of paper. Because of avoiding the complexity of rational LPV systems, the proposed controller can be applied to a robotic manipulator system or any non-singular LPV descriptor system without using rational LPV form.…”

“…Thus, we get the following inequality by also defining Remark: The inverse of   E  is a drastic case due to rational LPV form and there is no a formula for this, so an extra complexity occurs, and some assumptions or extra methods are needed as in [22,28,36,37]. For example, since…”

Fault diagnosis for a class of descriptor linear parameter‐varying systems

“…In fact, any region included inside the disk D(0, 1) can be chosen. However, if pole placement design is not considered, then the algorithm used to solve (41) could compute any H i , J i , L 2i and K satisfying the LMI (23), such that the matrices N i , i = 1, . .…”

“…Although the idea of merging descriptor and LPV systems is not new (see for instance [20]), there are very few works dealing with observer and controller synthesis, stabilization, fault diagnosis and other topics on automatic control for this kind of systems. Some recent papers on this topic dealing with the problem of control and stabilization are [21,22], whereas the authors in [23] address the problem of observer-based controllers.…”