Finite-time Control For Discrete-time Singular Markov Jumping Systems With Time-Varying Delay And Actuator Saturation

Discrete-time singular Markovian jumping systems have extensive applications,and with the development of computers,discrete-time singular Markovian jumping systems become more and more important.And we can find the application of this system in many practical systems,such as biological system,power system,economic system and so on.In recent years,finite-time control attracted many attentions of researchers and many researchers begin to study the problem of finite-time control for discrete-time singular Markovian jumping systems.The main purpose of this paper is to investigate the problem of finite-time control for discrete-time singular Markovian jumping systems.By constructing proper Lyapunov function,using differential inequalities,linear matrix inequality,and convex optimization methods,we have studied the problem of finite-time control for discrete-time singular Markovian jumping systems with time-varying delay and actuator saturation.The main results of this paper are as follows:Firstly,the problem of robust finite-time control for discrete-time singular Markovian jumping systems with input saturation and time-varying delay has been investigated.With proper Lyapunov function and linear matrix inequality and convex optimization methods,sufficient conditions that ensure the system finite-time bounded and finite-time H?bounded have been obtained.For H?is a particular situation of dissipative,as an option for system performance,in the chapter,we have studied the problem of finite-time dissipative control for discrete-time singular Markovian jumping systems with time delay and actuator saturation.In addition the transition rates are partly known.With delay-dependent Lyapunov function,some new criteria have been obtained that guarantee the systems finite-time bounded and finite-time dissipative.Then,we have investigated the problem that finite-time non-fragile memory control for discrete-time singular Markovian jumping system subject to time delay and input saturation.By constructing new Lyapunov function,sufficient conditions that ensure the systems finite-time bounded and finite-time H? bounded.In addition,the design method for non-fragile memory controller has been obtained.Finally,we have researched the observer-based finite-time control for discrete-time singular Markovian jumping systems.With new Lyapunov function and differential inequalities,we have got the criteria that ensure the system finite-time H? bounded,moreover,the corresponding observer and state feedback controller are obtained.