The Stability Analysis Of 2-D Discrete Systems

The stability of the two dimensions systems is studied.The systems including regular systems and singular systems are described by the Fornasini-Marchesini second local state-space models.In regular systems, the robust stability was studied for 2-D digital filters described by the Fornasini-Marchesini second local state-space model. Based on the definition of the robust stable margin, a frequency approach is proposed to estimate the stability robustness of a class of 2-D systems. And this menthod is compared with the former linear matrix inequality (LMI) method.It is also stressed that the use of 2-D LMI is limited in application to the stability robustness estimate problem of uncertain 2-D digital filters with saturation overflow arithmetic. Finally, an example is illustrated that it can be used in any 2-D system. It is also shown that the lower bound obtained by this algorithm is less conservative than the existing ones.In singular systems, the robust stability was studied for 2-D singular systems described by the Fornasini-Marchesini second local state-space model (SFM-II) with parameter uncertainty. Based on Lyapunov method, the stability of 2-D systems was discussed. Furthermore, under the condition of the acceptance of the closed-loop systems and no jump modes, a sufficient condition of the robust stability of SFM-II systems with uncertainty is presented via LMI. Finally, a desired algebraic transformation of state feedback control regularity is given by solving a set of matrix inequalities .So an effective way is given for the analysis and design of 2-D singular systems.