Finite-Time Almost Sure Stability of a Markov Jump Fuzzy System With Delayed Inputs

This article addresses the problem of finite-time almost sure stability, where the system is with Markov jump parameters and delayed inputs. With using Gronwall's inequality and strong law of large numbers for Markov chains, finite-time bounded criteria and finite-time stability criteria are derived by Lyapunov-Krasovskii functional method. Moreover, a finite-time stability criterion in form of linear matrix inequality is given to design the controller gain. The obtained results are applied to finite-time sampled-data control of a truck-trailer system and finite-time control of a Markov jump mass-spring model with delayed inputs.

Automated summary

This article addresses the issue of finite-time almost sure stability in systems with Markov jump parameters and delayed inputs. By utilizing Lyapunov-Krasovskii functional method, finite-time bounded criteria and stability criteria are derived, along with a linear matrix inequality for designing controller gain. The results are applied to finite-time sampled-data control and control of a Markov jump mass-spring model with delayed inputs.