Waqas Hussain,FA16-REE-006Dr. Mujtaba Jaffery, Assistant ProfesorLHR TP 56302026-04-102020https://hdl.handle.net/123456789/3383This thesis is concerned with stochastic stability of a class of non-linear discrete-time MJSs with time-varying delay, disturbance and partially unknown transition probabilities. By using linear matrix inequality approach and constructing proper Lyapunov-Krasovskii functional, sufficient criteria have been obtained that ensures the asymptotic stability of proposed system. By using the statae feedback controller, it is guaranteed that the state trajectories starting from a given region will remain in it even in the presence of disturbance, time-varying delay, where the non-linear fuction satisfy the one-sided Lipschitz and quadratically inner bounded conditions. In addition, second part of this research deals with the designing of observer-based controller which will stabilize the system without the requirement that the system states are measureable. Finally two examples are given to demonstrate the efficiency of the proposed design.endepartment of electrical engineeringFA16electrical engineeringstochastic stability of a class of non-linear discrete-timer matrix inequality approach and constructing proper Lyapunov-Krasovskii functionalsufficient criteria have been obtained that ensuresThesis