This work proposes a method to asses the local asymptotic stability and to provide polyhedral estimates of the region of attraction of the origin (RAO) of linear systems under aperiodic sampled-data control and saturating inputs. The approach is based on a discrete-time model that describes the behavior of the system state between consecutive sampling instants. It corresponds to a difference inclusion defined from a partition of the intersampling interval and from the saturated and nonsaturated (SNS) embedding of saturation functions. A method to construct a contractive polyhedral set for this model is proposed. It is shown that this set induces a local Lyapunov function strictly decreasing at the sampling instants and that it is an estimate of the RAO of the continuous-time closed-loop system.
This work presents a control design method for linear sampled-data systems whose random sampling intervals form a Poisson process. Unlike a previous result in the literature, the proposed stabilization conditions, based on linear feedbacks of both the state and the past input values, are necessary and sufficient for the mean exponential stability of the system. Moreover, such non-conservative conditions correspond to linear matrix inequalities, implying then that the stabilization problem can be efficiently addressed through semidefinite programming. As a second contribution, the characterization and optimization of the mean exponential convergence rate of the closed-loop system is given in form of a generalized eigenvalue problem. A numerical example illustrates the theoretical results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.