Mixed l-one/H-infinity control problem for discrete-time systems
离散时间系统混合l1/H∞-控制问题

This paper is concerned with mixed l-one/H-infinity-control problem of MIMO discrete_time systems where l-one-performance objective is minimized subject to an H-infinity constraint. By introducing an auxiliary optimal problem, we prove the continuous_dependence of optimal objective with respect to the constrainted H-infinity-performance objective. The existence of the solution of the auxiliary optimal problem is also proved. We present the convergence of the solutions of a series of the truncation problems of the auxiliary optimal problem, and show that its limit is the optimal solution of the auxiliary optimal problem. Particularly, we give an approach to obtain the converging lower and upper bounds of the mixed l-one/H-infinity-control problem. This approach gives a computationally efficient synthesis procedure which avoid the problem of zero-interpolation techniques. Finally, an example shows that the approach is feasible for designing suboptimal controller of the mixed control problem.