We suggest techniques based on set-invariance and Lyapunov theory, in particular piecewise-linear functions, to show that such models are amenable for robust investigation by engineers and mathematicians.
Based on the set invariance condition, an optimization approach is proposed to estimate the domain of attraction for the T S fuzzy delta operator systems.
Based on these set invariance conditions, the determination of the largest such ellipsoid, for use as an estimate of the domain of attraction, can be formulated and solved as an LMI optimization problem.
Then, based on the set invariance condition, this paper establishes H∞ stabilization conditions associated with a fuzzy weighting-dependent Lyapunov function, where the fuzzy controller is designed to be dependent on not only the current-time but also the one-step-past information on the time-varying fuzzy weighting functions.
In comparison with the existing approach based on conventional set invariance, the proposed approach results in a larger domain of attraction and better performance, both in the analysis of the closed-loop system under a given feedback gain and in the design of feedback gain.
For a discrete-time linear system subject to actuator saturation, an analysis and design approach based on Nth-step set invariance is proposed.
The method is based on the invariance of continuous-time Markov parameters.
Based on an invariance principle developed elsewhere, a discontinuous controller that uses only position measurement feedback is proposed.
The proofs are based on an invariance principle for Lyapunov-Razumikhin functions, which has been recently used to prove consensus between single integrator MAS.
Based on the invariance principle of stochastic differential equations and some suitable Lyapunov functions, several sufficient conditions are developed to solve this problem.
