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Paper details
Number 2 - June 2004
Volume 14 - 2004
A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy
Jerzy Tokarzewski
Abstract
The question how the classical definition of the Smith zeros of an LTI continuous-time singular control system S(E,A,B,C,D) can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with a nonzero state-zero direction. Such a definition allows an infinite number of zeros (then the system is called degenerate). A sufficient and necessary condition for nondegeneracy is formulated. Moreover, some characterization of invariant zeros, based on the Weierstrass-Kronecker canonical form of the system and the first nonzero Markov parameter, is obtained.
Keywords
singular control systems, multivariable zeros, state-space methods, Markov parameters