Controllability Analysis Of Discrete-Time Linear Time-Delay Systems With Noise

This paper deals with the controllability analysis of discrete-time linear time-delay sys-tems with noise by a data-based method. The controllability of time-delay systems is deter-mined by the existence of an input vector which can drive the system from any initial state and any initial input to any final state in finite steps. By introducing a new concept, the min-imum controllability realization index (MinCRI), the controllability feature of delay systems is discussed. Besides, a data-based method can directly construct a controllability matrix us-ing the measured state data to analyze the controllability of systems without identifying system parameters. Hence, it can save time in practice and avoid corresponding identification errors. Moreover, its calculation precision is higher than some other traditional approaches, which need to identify unknown parameters. Data-based method are feasible to the study of characteristics of deterministic systems.First, a data-based method is used to construct controllability matrix for analyzing the con-trollability of systems. Second, taking into account of noise in the systems and the measured data in real applications, this paper discusses the controllability criteria with noise. The unbi-asedness and consistency of this estimate with measurement noise and system noise are proven, respectively. Finally, this paper deals with precision of tradition method and data-based method, and gives a numerical example to show the advantage of the results.