Studies on stability and stabilization of dynamical control systems

Abstract

This thesis reports the studies on stability and stabilization of various kinds of dynamical control systems. In particular, it considers control systems which can be described by switched systems, stochastic systems, Markovian jump systems, neutral systems and Takagi-Sugeno fuzzy systems. These systems under study are subject to time delay, environmental disturbances, actuator constraints, nonlinearities and uncertainties. The key focus in the thesis is to design appropriate controllers such that the considered dynamical systems are not only stable and robust, but also satisfies a prescribed performance level. The various controllers discussed includes fault-tolerant control, sampled-data control, H¥ control, passivity-based control and resilient control. Using Lyapunov stability theory, set of sufficient conditions are derived to obtain the required results. Such conditions are established using linear matrix inequality approach, Newton-Leibniz formula, free-weighting matrices approach, average dwell time approach, Jensen s inequality, Wirtinger-based inequality and various other analysis techniques. In the study of stability analysis, first, reliable stabilization of switched dynamical systems is considered. Further, resilient control design and mixed H¥ and passivity-based control design are addressed for Markovian jump and stochastic dynamical systems. Later, finite-time stability analysis and control design for dynamical systems subject to actuator faults and controller gain fluctuations are discussed. Then, resilient fault-tolerant control design is proposed for Takagi-Sugeno fuzzy systems subject to actuator saturation. newline newline newline