Autonomy, forward non-Zenoness and quadratic stability
of bimodal higher-order piecewise linear systems
Autonomy, forward non-Zenoness and quadratic stability
of bimodal higher-order piecewise linear systems
We consider bimodal higher-order piecewise linear systems, i.e. the sets of solutions of two higher-order linear differential equations, coupled with inequality constraints involving a polynomial differential operator acting on the trajectories of the system. Under suitable assumptions on the characteristic polynomials of the differential equations and the polynomial associated with the inequality constraint, we prove that a solution always exists and is unique given the initial conditions, that no forward Zeno-behavior is possible, and that the system is quadratically stable. Moreover, we provide an algorithm based on polynomial algebra to compute a Lyapunov function for the system.
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Camlibel, M.K.
de670aa3-6a3e-4a7b-8a78-0b58189080ab
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Camlibel, M.K.
de670aa3-6a3e-4a7b-8a78-0b58189080ab
Rapisarda, Paolo and Camlibel, M.K.
(2014)
Autonomy, forward non-Zenoness and quadratic stability
of bimodal higher-order piecewise linear systems.
IEEE: 53rd Conference on Decision and Control, , Los Angeles, United States.
15 - 17 Dec 2014.
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Conference or Workshop Item
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Abstract
We consider bimodal higher-order piecewise linear systems, i.e. the sets of solutions of two higher-order linear differential equations, coupled with inequality constraints involving a polynomial differential operator acting on the trajectories of the system. Under suitable assumptions on the characteristic polynomials of the differential equations and the polynomial associated with the inequality constraint, we prove that a solution always exists and is unique given the initial conditions, that no forward Zeno-behavior is possible, and that the system is quadratically stable. Moreover, we provide an algorithm based on polynomial algebra to compute a Lyapunov function for the system.
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e-pub ahead of print date: December 2014
Venue - Dates:
IEEE: 53rd Conference on Decision and Control, , Los Angeles, United States, 2014-12-15 - 2014-12-17
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Local EPrints ID: 373820
URI: http://eprints.soton.ac.uk/id/eprint/373820
PURE UUID: 4af59150-929c-45b8-b206-e3ef8ed47123
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Date deposited: 03 Feb 2015 15:40
Last modified: 14 Mar 2024 18:58
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Author:
Paolo Rapisarda
Author:
M.K. Camlibel
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