Relaxed Static Output Stabilization of Polynomial Fuzzy Control Systems
by Lagrange Membership Functions
This paper is concerned with the stability analysis of the static
output-feedback polynomial fuzzy-model-based (SOF PFMB) control systems
through designing a novel membership grade integration (MGI) approach.
The nonconvex problems of the SOF PFMB control systems are
convexificated into the convex conditions by introducing block diagonal
positive-definite Lyapunov matrix and nonsingular transformation matrix.
We proposed a new approximated membership functions, i.e. Lagrange
Membership Functions (LMFs) method, which can be introduced into the
stabilization process to relieve the stability conservativeness results.
The LMFs are general representations of piecewise-linear membership
functions (PLMFs), which makes the number of stability conditions not
limited by the number of sample points. In a fixed subdomain, arbitrary
sample points can be employed by the LMFs method and achieve higher
approximation capability by increasing more sample points, so that
membership grades can be incorporated into the system analysis.
Furthermore, a novel MGI approach including the information of premise
variables and LMFs are proposed, which can make the stability conditions
more relaxed. Finally, a simulation example is given to show the merits
of the developed techniques.