Fault-Tolerant Control For Delta Operator Switched Systems

Switched systems control is a hot class of control theory,of which the research results are very plentiful.But there exist many problems havenot been solved completely,such as fault-tolerant contol.In digital control,delta operator is better than shift operator,so that delta operator systems go in the view of many researchers.A switched system,of which each mode is described as a delta operator system,is called a delta operator switched system.In recent years,delta operator switched systems are just in the eyes of some scholars.So the control theory of delta operator switched systems has a great potential to develop.For practical switched systems with faults,not only it is needed that the closed-loop stability under the designed controller and switching law,but also some other performances,such as the less affectiveness from external disturbance to regulated output,etc.This paper is devoted into the research of fault-tolerant control problems of delta operator systems.What this paper done is introduced as follows.(1)For a class of robust delta operator systems with actuator faults,the robust guaranteed-cost H_? reliable control problem is dealt with.Based on arbitrary switching and state switching approaches,the state feedback controller and the switching law are designed to guarantee that the closed-loop switched system has a specified H_? performance and an upper bound of the closed-loop cost function is provided.In the design process,an approach of dealing with the uncertain matrices multiplying phenomenon appears in this problem.(2)The non-fragile reliable(35)-stabilization problem of a class of delta operator switched linear sys tems with actuator faults is concerned,in terms of linear matrix inequalities(LMIs).Firstly,to handle the determination problem of the decay rate of each mode of the delta operator switched system in the process of(35)-stabilizing,the theory of first-order LMI regions is proposed.Secondly,to deal with the uncertain matrices multiplication phenomenon appearing in non-fragile reliable control,a new approach is proposed.Based on the average dwell time approach and the two new approaches mentioned above,the state feedback controller and the switching law are designed to guarantee that all the closed-loop poles of each mode lie in a specified disk and the closed-loop switched system is exponentially stable.(3)The reliable guaranteed-cost control problem for a class of delta operator switched linear system s with actuator faults is settled,in terms of mode-dependent average dwell time(MDADT)approach.Firstly,based on MDADT approach,asymptotical and exponential stabilities of delta operator nonlinear switched systems are analyzed.Then,the reliable controller and the minimum MDADT are designed to stabilize the considered delta operator linear switched system with actuator faults and to determine an upper bound of the given cost function.(4)The fault detection and fault-tolerant control problem of delta operator switched systems is dealt with.Based on state switching approach,a switching observer/controller and the state switching law are designed to detect the fault and to guarantee a specified closed-loop H_? performance.(5)A dynamic output feedback fault-tolerant control design problem of a class of delta operator line ar systems with sensor faults is studied by dynamic output feedback and two state switching control approaches in terms of linear matrix inequality(LMI)technique.Firstly,the Lyapunov-Metzler inequalities approach is used.The nonzero elements of the Metzler matrix are utilize directly to design the switching controller and the switching law.Secondly,the convex combination approach is also utilized to design the state switching law.The controller and switching law designed by the two approaches above can guarantee the asymptotical stability of the closed-loop switched system.In the convex combination approach,there exists a multiplying phenomenon of uncertain matrices.An effective method of dealing with this phenomenon is proposed.(6)Based on state switching approach,the reliable H_? control problem with dick pole constraint is solved for a class of delta operator switched systems with actuator faults.Lyapunov-Metzler approach and convex combination technique are employed respectively to design the state feedback controller and the switching law to guarantee that all of the closed-loop poles of each mode of the switched system lie in a specified disk and the closed-loop switched systems possesses an appointed H_? performance.