- Title
- External positivity of linear systems: Approximate characterization via convex polytopes
- Creator
- Weller, Steven R.
- Relation
- 22nd IFAC World Congress. Proceedings of the 22nd IFAC World Congress: Proceedings [presented in IFAC-PapersOnLine, Vol 56 (2)] (Yokohama, Japan 09-14 July, 2023) p. 5077-5082
- Publisher Link
- http://dx.doi.org/10.1016/j.ifacol.2023.10.1289
- Publisher
- Elsevier
- Resource Type
- conference paper
- Date
- 2023
- Description
- A linear system is said to be externally positive if the system output is non-negative for all time when driven by a non-negative input from the zero initial state. External positivity is well known to be equivalent to non-negativity of the impulse response and hence monotone nondecreasing step response. Despite the apparent simplicity of characterizing systems with nonnegative impulse response, the determination of necessary and sufficient conditions for external positivity from a given transfer function is a long-standing open problem. In this paper, we propose a method which approximately characterizes the true region capturing the numerator polynomials of all (strictly proper) externally positive linear systems whose specified poles are assumed to satisfy a known necessary condition for external positivity. We compute an (outer) approximation of the true region via the construction of a convex polytope, each facet of which is contained in a supporting hyperplane of the true region. The proposed method requires only modest computational effort; has an accuracy which can be increased readily; applies to systems having orders n ≥ 4 for which no general characterizations of external positivity are currently known; and handles systems with complex poles (possibly repeated). Numerical examples illustrate the effectiveness of the proposed method.
- Subject
- positive systems; linear systems; impulse response; convex polytope
- Identifier
- http://hdl.handle.net/1959.13/1502350
- Identifier
- uon:55224
- Identifier
- ISBN:9781713872344
- Language
- eng
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