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2 International Journal of Applied Mathematics and Computer Science

2 Tokarzewski J.

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A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy

Tokarzewski J.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 2

149-159

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.

A general solution to the output-zeroing problem for MIMO LTI systems

Tokarzewski J.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 2

161-171

The problem of zeroing the output in an arbitrary linear continuous-time system S(A,B,C,D) with a nonvanishing transfer function is discussed and necessary conditions for output-zeroing inputs are formulated. All possible real-valued inputs and real initial conditions which produce the identically zero system response are characterized. Strictly proper and proper systems are discussed separately.