| Actual engineering systems mostly are nonlinear and the most common one of them is Lipschitz system,that is,the nonlinear function satisfies the Lipschitz condition.In fact,the existing results on Lipschitz systems are applicable just for small enough Lipschitz constants.In order to improve the situation,the one-sided Lipschitz(OSL)condition and the quadratic innerbounded condition were introduced to reduce the conservativeness of the system.It is known that many systems affected by uncertain matrices,uncertain parameters and noise interference.Thus,it is necessary to study the robustness of the systems.Besides,we often control the systems based on the estimated states given by the observer,because that the systems states can not be obtained completely.Therefore,the design methods of robust observer and controller for uncertain OSL systems are discussed in this paper.We will consider uncertainties which not only exist in the state and output matrices,but also in the nonlinear function.For the given systems,we will discuss two kinds of control methods(feedback control、sliding mode control)and two kinds of stabilities(stochastic stability、finite-time stability).The main research works are as follows:1.We will study the problem of robust observer and H∞ controller design for a class of uncertain OSL Markovian jump systems.Firstly,we will describe the systems and design observer and observer-based feedback controller for them.Then,we can obtain the form of closed-loop systems and clear the final control objective.Next,we will give some sufficient conditions,which ensure the robust stochastic stability of the closed-loop systems.Based on these,the H∞ performance will be considered and the sufficient conditions which guarantee the robust H∞ stochastic stability of the closed-loop systems will be presented.After that,we will transform inequalities as the sufficient conditions into linear matrix inequalities(LMIs)and solve observer and controller matrix gains at the same time.Then,the optimization strategy will be given for some meaningful indexes,and the corresponding optimization problem will be obtained.Finally,we will discuss a numerical example to demonstrate the effectiveness of the design methods.2.We will study the problem of robust observer and finite-time H∞ controller design for a class of uncertain singular OSL systems.Firstly,we will describe the systems in detail and design observer and observer-based feedback controller.Then,we can obtain the form of closed-loop systems and clear the final control goal.Next,we will prove that the closedloop systems are regular,impulse-free and finite-time boundedness.Based on these,several sufficient conditions will be presented which ensure robust H∞ finite-time boundedness of the closed-loop system.Then,these sufficient conditions will be expressed by a set of LMIs and the solutions of matrix gains will be given.In the end,we will optimize several important indexes in regards to our research and get the optimization problem to be solved.Two concrete examples will be used to illustrate the effectiveness of the design methods.3.We will address the problem of robust observer and finite-time sliding mode controller design for a class of uncertain OSL systems.At first,we will describe these systems and design observer and observer-based integral-type sliding surface.Then,it can be proved that the estimated states can reach the preset sliding surface under the given sliding mode control(SMC)law in a finite time interval.Afterwards,we will analyze the finite-time boundedness of the corresponding closed-loop system in the reaching phase and the sliding motion phase,respectively.Next,we will give the sufficient conditions in terms of LMIs,which guarantee that the closed-loop systems are finite-time boundedness in the whole time interval.Meanwhile,the design methods of observer and controller matrix gains will be presented.After that,we will pay attention to two important indicators,and get a constrained optimization problem.Finally,two examples will be given to test the effectiveness of the design methods. |
