Exponential Stability In Mean-square Of Markovian Jump Systems With Saturating Actuators And Time-varying Delay

Most practical control systems, nonlinear parts or components contain nonlinearfactors. Nonlinear factors, which can lead to be instability, have influenced theperformance of the system. Especially, with saturated the implementation of thesystem, the saturation is the implementation of the nonlinear systems. Along withthe development of the nonlinear theory, people gradually realize the limitations oflinear system theory results. For example, although in theory we can designfeedback control but unbound, which achieve stability. However, in the actualsystems, actuators or inputs with saturation can be reason of poor performancebehavior or closed-loop instability. In modern control theory, the system controllerinput is considered to be unbounded. Thus, the saturated implementations areignored. However, the above mentioned method, if designed control input exceedsthe limitation of the actual system, the performance of closed-loop system suddenlydrop, or results in very serious consequences. In recent years, stability of thesystem with saturated actuator has received more attention, which is one ofsignificant fields of the theory of control systems and its application. However,little research work was devoted to the classical systems, such as bilinear andsingular systems. Therefore, this paper will investigate stability of these typicalsystems in the saturated state of the input.This dissertation provides the following two results on systems with saturatingactuators:a) We investigate exponential stability in mean-square of stochastic bilinearsystems with saturating actuators. The system is described by state differentialequation with Markovian jump and time-varying delay in state and input. Asufficient condition is proposed for exponential stability in mean-square of thesystem using Lyapunov-Krasovskii theory.b) We investigate exponential stability in mean-square of singular markovianjump systems with saturating actuators and time-varying delay. The statistical ofthe Markov process is fully used to derive the differential of the functional. Basedon using a delay decomposition method, construct a mode-dependent Lyapunov-Krasovskii function. A sufficient condition is proposed for exponential stability inmean-square of the system designing the memory less state feedback.