On Stability Of Zeros Of Discrete-time MIMO System With PC GSHF

Zeros play an important role in control-system design. It is well-known that unstable zeros limit the perfermance that a control system can be achieved. When a continuous-time system is discretized by the use of a sampler and a hold,stable zeros can not be mapped inside unit circle,this means that the stability of zeros is not necessarily preserved. Different signal reconstruct device will influence the position of zeros,so special attention has been paid to the study on the stability of the zeros of discrete-time systems.The paper is supported by China National Natural Science Foundation item"Study on the stability of the zeros of the discrete-time MIMO(multi-input multi-output)system with multirate input and hold". First,we study on the stability of the zeros of the discrete-time SISO system with PC GSHF(piecewise-constant generalized sampled-data hold),the minimum number of segments of PC GSHF for stable zeros are derived.Then, the stability of the zeros of the continuous-time MIMO system with the degrees of the infinite elementary divisorsμ1 =…=μ_m-k=μ,μ_m-k+1=…=μ_m=μ+ 1 ( k = 1,…, m,μ= 3)with PC GSHF when Tâ†'0 is studied,and the stability conditions for limiting zeros when N =μis derived.Finally, the simulation of discretized time model tracking control based on a SISO system and a 2-input 2-output system is researched. The results show that by choosing the proper parameters the stability of the MIMO system zeros can be preserved, PC GSHF indeed displays more superiorities to ZOH for the stability of the zeros.