【摘要】 本文利用一般离散系统的Lyapunov方程研究了灰色离散系统的稳定性问题,并给出了灰色离散系统的稳定性充分判据和应用实例。更多还原

【Abstract】 The stability of grey discrete-time systems (discrete-time systems with uncertain parameters or interval discrete-time dynamic systems) is discussed in terms of Lya-punov’s stability theorem for ordinary discrete-time systems and Perron-Frobenius theorem. Several sufficient criteria for the stability of grey discrete-time systems are presented.The grey discrete-time system discussed is described by the following expression: X(k + 1)=A()X(k), X(0)=X0, (1)where A() is an n×n real matrix and its elements ij are not exactly known and may even vary with time. However, the eij and fij (i,j) and the relationships ij∈[eij, fij] are known.One of the main criteria is as follows:Suppose Q is an n×n symmetric positive-definite matrix. Grey discrete-time system (1) is asymptotically stable if the solution p of matrix equation Q = P-ATPA is symmetric positive-definite and the matrix inequalities p-I>0 and Q - βI + ATA-P + I-p-1>0 hold. Here A=[αij]n×n=[(eij+fij)/2]n×n; β = ρ(HTH), H= [hij]n×n = [fij-αij]n×n; ρ(·) is the spectral radius of matrix · and · >0 denotes the positive-definite ness of matrix.更多还原