Robust integral feedback control based on interval observer for stabilising parameter‐varying systems

Stabilizing a class of nonlinear parameter‐varying systems using interval observer based on a piecewise framework

“…Although it is hard to find global solution for the inequality (31), some innovative iterative methods such as linearization, 49 P‐K iterations, 50 and path‐following 51 developed in literature to find local solutions for these problems. Here, inspired by References 33,52, we want to present an iterative approach to solve the inequalities Equations (30) and (31). Let consider $$$ {K}_1={\mathcal{K}}_1^{-1}{\mathcal{L}}_1+{K}_1(j) $$$ and $$$ {K}_2={\mathcal{K}}_2^{-1}{\mathcal{L}}_2+{K}_2(j) $$$, where $$$ {K}_1(j)\in {\mathbb{R}}^{m\times 2n} $$$ and $$$ {K}_2(j)\in {\mathbb{R}}^{m\times r} $$$ are the value of these gains with iteration $$$ j $$$ and $$$ {\mathcal{K}}_1\in {\mathbb{R}}^{m\times m} $$$, $$$ {\mathcal{K}}_2\in {\mathbb{R}}^{m\times m} $$$, $$$ {\mathcal{L}}_1\in {\mathbb{R}}^{m\times 2n} $$$, $$…”

“…Looking for such gains is very conservative and decreases the feasibility of the matrix inequalities especially when the number of regions increases. This issue is relaxed to some extent in Reference 33 by using PLF approach. Second, even though the outputs of the parameter‐varying system are measurable, to the best of our knowledge, the existing interval‐observer‐based control methods have not used them in their control signals.…”

Finite‐time functional interval observer for linear systems with uncertainties

“…Moreover, based on the system internal positive representations, the novel structure of an IO is exploited to both discrete and continuous‐time systems without any changes of coordinates in [10]. Meanwhile, Wang et al [11] developed a gain‐scheduled IO for the linear parameter‐varying systems with polytope uncertainty, and in the framework of the IOs, the robust integral feedback stabilising controller is proposed for the parameter‐varying systems in [12]. Besides, an IO is constructed in [13] using the D‐similar transformation proposed in the earlier works of Zhu and Johnson [14] for time‐varying systems.…”