Abstract

The conditions that function We(z), which ensures the minimum acceptable time of the switching process, must satisfy can be formulated as follows: — function We(z) should have nulls equal to the poles of Wn(z) positioned in the unit circle or outside of plane z; — function W(z) or 1 — We(z) should have all nulls of Wn(z) located in the unit circle or outside of plane z as nulls; — function W(z) or 1 — We(z) should contain z−1 as cofactor z−1. If Wn(z) is an unstable unit impulse response, then F(z) should contain all poles of Wn(z) lying in the unit circle or outside of plane z as nulls (with the exception of the poles for z = 1). If Wn(z) has nulls located in or outside of the unit circle, these nulls must be nulls of W(z) = 1 − (1 − z−1). In these two cases, the briefest time of the switching process will exceed the value which can be obtained for a system with a stable unit impulse response Wn(z) which has no nulls in or outside of the unit circle of plane z.

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