Studies On Singularly Perturbed Control Systems With Delay And Jump

This dissertation is devoted to the problems passivity-based sliding mode control(SMC)of singularly perturbed systems with time-delay,sliding mode control for Markovian switching singularly perturbed system,and passivity-based sliding mode control(SMC)for Lur'e singularly perturbed time-delay systems with input nonlinearity.A singularly perturbed system is two-time-scale structure,which often leads to the increased order and stiffness of systems.This poses formidable computational complexities for the analysis and control of the systems.For these problems,the singular perturbation was put forward,which has been a highly recognized and rapidly developing area of control systems in the last years.These systems often occur naturally because of the presence of small parasitic parameters multiplying the time derivatives of the system states.Markovian jump singularly perturbed control systems have been intensively studied for the past few decades.Recently it has gained a great achievement in developing systematic,theoretical rigorous techniques for analyzing and designing the problem of singularly perturbed systems.As sliding mode control;it needs further investigation and improvement on the passivity analysis of singularly perturbed systems with time-delay.Based on the recent research on the theory of the Markovian jump singularly perturbed system,this dissertation investigated the passivity and passification based on sliding mode control for singularly perturbed systems and nonlinearity Lur'e singularly perturbed time-delay systems,in addition of sliding mode control for Markovian switching singularly perturbed systems and gives some new results.To sum up,the major works in this dissertation are as follows:1-Firstly,passivity analysis and passivity-based SMC for a class of singularly perturbed time-delay system presented.This result is pay particular attention to the singular perturbed matrix E? to the design of an integral-type switching surface function.Which leads to a full-order singularly perturbed time-delay systems for describing the sliding mode dynamics.We then apply the slack matrix approach to derive a delay-dependent sufficient condition in the form of linear matrix inequality(LMI),which guarantees that the sliding mode dynamics is generalized quadratically stable and robustly passive.In addition also we studied how to solve the passification problem.Finally,we investigated the synthesis of a SMC law or an adaptive SMC law for driving the system trajectories onto the predefined switching surface in a finite time.2-The sliding mode control(SMC)for Markovian switching singularly perturbed systems is investigated.The sliding mode controller is designed to guarantee that the nonlinear singularly perturbed systems are stochastically admissible and its trajectory can reach the sliding surface in finite time.By used Lyapunov functional methods,some criteria on stochastically admissible are established in the form of linear matrix inequalities(LMIs).3-The passivity-based sliding mode control(SMC)for Lur'e singularly perturbed time-delay systems with input nonlinearity proposed.A novel ?-dependent switching surface function is designed such that resulting sliding mode dynamics is still a singularly perturbed system.Based on a linear matrix inequality(LMI)technique,delay-dependent and delay-independent sufficient conditions are proposed respectively,under which the sliding mode dynamics is passive and asymptotically stable.The criteria of both independent of the small parameter and the upper bound for the passivity obtained in a workable computation way are presented.Then,a SMC law is designed to guarantee that the system state can be driven onto the specified switching surface in a finite time and stays there for all subsequent time.This dissertation is the one of a few researches work in the current literature to use passivity analysis and sliding mode control to study the singularly perturbed systems and Lur'e singularly perturbed time-delay systems with input nonlinearity and Markovian switching singularly perturbed system using LMI condition technique.It is our hope that this work will pave the way for further studies on the passivity-based sliding mode control for singularly perturbed systems.