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Kučera, Vladimír

Internal properness and stability in linear systems. (English) Zbl 0596.93050

Kybernetika 22, 1-18 (1986).
The author examines the concept of internal properness for generalised state space systems. Starting from the requirement that ”stability” for such systems dictates that for certain class of external inputs and/or disturbances the ”generalized state” and ”output” vectors must behave according to a certain acceptable behaviour at \(t=0\) and \(t=\infty\), the author looks at the concept of internal properness as the dual of that of internal stability. This is done by regarding the stability of such systems as defined by the location in the extended complex plane of the finite and infinite zeros of the characteristic matrix sE-A associated with such systems. Thus while acceptable behaviour at \(t=\infty\) necessitates that all finite zeros of sE-A lie in the open left half complex plane: \(Re(s)<0\), acceptable behaviour at \(t=0\) (i.e. absence of impulsive behaviour at \(t=0)\) imposes the requirement that sE-A has also no zeros at \(s=\infty.\)
Based on this duality between finite and infinite zeros of sE-A, the author examines various problems of synthesis of feedback systems. These include the ”disturbance rejection” problem, the exact model matching problem, output regulation, block decoupling etc.
Reviewer: A.Vardulakis

Cited in 10 Documents

MSC:

93D99 Stability of control systems
34A99 General theory for ordinary differential equations
93C05 Linear systems in control theory
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
34D30 Structural stability and analogous concepts of solutions to ordinary differential equations
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics

Keywords:

internal properness; generalised state space systems; internal stability; finite and infinite zeros; feedback systems
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\textit{V. Kučera}, Kybernetika 22, 1--18 (1986; Zbl 0596.93050)

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