Robust Control Of Semi-Markov Jump Systems With Linear Fraction Uncertainty

Physical processes which are governed by differential equations or difference equations with discontinuous behavior can be modeled as jump systems. Such as networked control systems, fault tolerant control systems, and other systems subject to abrupt changes. The Semi-Markov jump system is more extensive and complex than Markov jump system.The research of the dissertation involves the robust stochastic stability, robust state feedback and robust dynamic output feedback for a class of continuous-time Semi-Markov jump linear systems with linear fractional uncertainties.The principal research contents are listed as follows:1. Robust stability problem for a class of continuous-time Semi-Markov jump linear systems with linear fractional uncertainties is investigated based on multiple Lyapunov function techniques and LMI approach. Developed conditions can be used to check a dynamical system is of robust stochastic stability or not.2. For the given conditions with linear fractional uncertainties Semi-Markov jump linear system for the robust stability, there are much inconvenience in the numerical examples when they are proved. This paper converts sufficient conditions to the appropriate forms of expression by convex combination principle, and proves the correctness of the results through providing suitable numerical examples.3. In order to reduce the conservatism of the numerical examples with stability conditions, it will make the Semi-Markov jump linear systems in each division interval is an independent system through partitioning the sojourn-time h into M sections and reduce the conservatism effectively.