Singular systems are of more universality and extensive applications compared with reg-ular ones, and they widely exist in many fields such as economics, network systems, robot systems, and so on. There are numerous results relating to control theory research of singular system, many of which are derived based on study methods of regular systems, whereas the control of singular systems is more complicated and needs to consider the conceptions such as regularity and causality. Control of singular systems with uncertainties and disturbances is a significant topic in modern control theory. In addition, control of singular systems with time delay is also a hot area of robust control research.This dissertation studies the H_∞ control of discrete-time singular systems with time de-lays and uncertainties by applying sliding mode control approach. A design method of sliding mode controller is given to guarantee that the systems satisfy H_∞ performance. Numerical simulations illustrate the effectiveness of the proposed approach. Specific study contents are as follows:(1) For uncertain discrete-time singular systems with matched disturbance and mismatched disturbance, a new type of integral sliding mode containing singular matrix is proposed, and then a design method of equivalent controller is presented to make the sliding mode satisfies H_∞ performance. Besides, on the basis of linear discrete-time reaching law and the estimation of disturbance, a new control rule, which ensure that the systems reach quasi-sliding surface with bounded bandwidth within finite time, is designed, and the bound of quasi-sliding surface bandwidth is given. A numerical example elucidates the effectiveness of the proposed design approach.(2) For uncertain discrete-time constant time delay singular systems with matched distur-bance and mismatched disturbance, a new type of integral sliding mode containing singular matrix E and the delay term is proposed, and then a design method of time delay dependent equivalent controller is presented to make the sliding mode satisfies H_∞ performance. Besides, on the basis of linear discrete-time reaching law, a new control rule, which ensure that the sys-tems reach quasi-sliding surface with bounded bandwidth within finite time is designed, and the bound of quasi-sliding surface bandwidth is given. A numerical example elucidates the effectiveness of the proposed design approach.(3) For uncertain discrete-time time-varying delay singular systems with matched distur-bance and mismatched disturbance, a new type of integral sliding mode containing singular matrix E is proposed, and then a design method of time delay dependent equivalent controller is presented to make the sliding mode satisfies H_∞, performance. Besides, on the basis of linear discrete-time reaching law, a new control rule, which ensure that the systems reach quasi-sliding surface with bounded bandwidth within finite time, is designed, and the bound of quasi-sliding surface bandwidth is given. A numerical example shows the effectiveness of the proposed design approach. |