Stabilization of uncertain dynamical systems via state feedback control

Abstract

The research work recorded in this thesis focuses on the stabilization of various kinds of uncertain dynamical systems via a state feedback controller design. Predominantly, this thesis attempts to showcase some research developments on state feedback controller design for uncertain dynamical systems which are described by switched time-delay systems, Takagi-Sugeno fuzzy time-delay systems, stochastic time-delay systems, fractional-order systems and biological economic systems. Moreover, effects of parameters such as nonlinearities, actuator faults which may be linear or n onlinear, input saturation and environmental disturbances on these uncertain dynamical systems are also studied. The main idea behind this thesis, is to establish stability and stabilization of control systems via various kind of state feedback control strategies, namely, reliable control strategy, equivalent input disturbance-based tracking control strategy, passivity-based control strategy, finite-time control strategy and resilient control strategy. By employing the concepts of Lyapunov stability theory, some sufficient conditions for the stability of the considered uncertain dynamical systems are procured. These procured sufficient conditions are developed using Jensens inequality and linear matrix inequality approach. In this thesis, the problem of stabilization for switched delta-operator time-delay systems and switched nonlinear systems with multiple time-varying delays are initially considered. Additionally, passivity based reliable stabilization problem for a class of Takagi-Sugeno fuzzy time-delay systems are discussed. Further, reliable stabilization problem is discussed for an asymmetrically constrained stochastic interval system with time-delay. newline