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Numerical robustness of COVID-19 model with Lyapunov stability analysis. [PDF]

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Pandey A, Ghosh S.
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Stability of piecewise linear systems revisited

Annual Reviews in Control, 2010
Abstract Piecewise linear systems are important in representing and approximating many practical systems with complex dynamics. While stability analysis of switched linear systems are notoriously challenging, several powerful tools have been developed to cope with the challenges.
Zhendong Sun
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Singular perturbation in piecewise-linear systems

IEEE Transactions on Automatic Control, 1988
This note analyzes piecewise-linear systems which are singularly perturbed. A technique is developed that allows decoupling of such systems into fast and slow subsystems for analysis and design. The results of a numerical example are included to demonstrate this technique.
Heck, B. S., Haddad, A. H.
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Linear conjugacy of n-dimensional piecewise linear systems

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1994
Summary: A proof is given that \(n\)-dimensional systems characterized by a piecewise linear continuous vector field with odd symmetry and three linear regions are linearly conjugate if their sets of eigenvalues are identical. For this the eigenvalues in the inner region are assumed to be pairwise distinct.
Feldmann, Ute, Schwarz, Wolfgang
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Controllability of piecewise linear systems

Systems & Control Letters, 1986
The paper gives a necessary and sufficient condition for the local controllability of a discontinuous linear control system. The set of discontinuities is a hyperplane S. The system is defined by two different linear time-independent equations on the two closed halfspaces defined by S.
Veliov, Vladimir M., Krastanov, Michail I.   +1 more
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Piecewise-Linear Approximation of Nonlinear Dynamical Systems

IEEE Transactions on Circuits and Systems I: Regular Papers, 2004
The piecewise-linear (PWL) approximation technique developed by Julia/spl acute/n et al. in the past few years is applied to find approximate models of dynamical systems dependent on given numbers of state variables and parameters. Referring to some significant examples, i.e., topological normal forms, it is shown that a PWL dynamical system ...
STORACE, MARCO, DE FEO OSCAR
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Structured analysis of piecewise‐linear interconnected systems

International Journal of Robust and Nonlinear Control, 2007
AbstractThis paper considers the problem of assessing the induced L2gain of a system composed of non‐identical interconnected piecewise‐linear subsystems, when the topology of the underlying graph is arbitrary. Blending tools inspired by dissipativity theory and theS‐procedure, it presents sufficient conditions in the form of a set of finite ...
Fowler, Jeffrey M., D'Andrea, Raffaello
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BIMODAL PIECEWISE LINEAR DYNAMICAL SYSTEMS: REDUCED FORMS

International Journal of Bifurcation and Chaos, 2010
Piecewise linear systems constitute a class of nonlinear systems which have recently attracted the interest of researchers because of their interesting properties and the wide range of applications from which they arise. Different authors have used reduced forms when studying these systems, mostly in the case where they are observable. In this work, we
Ferrer, Josep, Magret, M. Dolors, Peña, Marta   +2 more
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Stabilization of orthogonal piecewise linear systems using piecewise linear Lyapunov-like functions

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 2002
In this paper the problem of asymptotic stabilization of orthogonal piecewise linear (OPL) systems is considered. OPL systems arise when the state-space is partitioned into a number of distinct regions by hyperplanes orthogonal to the states. Different regions possess different continuous linear affine dynamics.
C.A. Yfoulis, A. Muir, N.B.O.L. Pettit, P.E. Wellstead   +3 more
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