Open AccessStability and stabilisation of heterogeneous switched systems with arbitrary switching constraints
Author(s) -
Yu Shaohang,
Wu Chengfu,
Wu JiaNan,
Wang Liang
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2019.0853
Subject(s) - control theory (sociology) , lyapunov function , diagonal , mathematics , block (permutation group theory) , stability (learning theory) , controller (irrigation) , polynomial , computation , mathematical optimization , computer science , control (management) , algorithm , nonlinear system , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
Heterogeneous switched systems are a class of special hybrid systems containing different dimensional subsystems. To research the stability and stabilisation of heterogeneous switched systems, a novel approach is presented to design static output feedback controllers for asymptotically stabilising heterogeneous continuous‐time and discrete‐time switched systems under arbitrary switching rules. This approach, which has less computation complexity, includes a main diagonal square block common Lyapunov function for stability analysis of heterogeneous switched systems and a main diagonal square block common homogeneous polynomial Lyapunov function for stabilisation of heterogeneous switched systems. In the study of stabilisation of heterogeneous switched systems, a two‐step iterative method including two convex optimisation functions is established by sums of squares to express existing properties condition and solvable properties condition for determining block controller. At last, a practical example and two numerical examples are presented to show the feasibility of the proposed results.