Synthesis of dissipative systems using quadratic differential forms: Part I [PDF]
IEEE Transactions on Automatic Control, 2002 In this second part of this paper, we discuss several important special cases of the problem solved in Part I. These are: disturbance attenuation and passivation, the full information case, the filtering problem, and the case that the to-be-controlled plant is given in input–state–output representation.
Trentelman, H.L., Willems, Jan C.
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STABILITY OF NONLINEAR DYNAMICAL SYSTEM MOTION UNDER CONSTANTLY ACTING PERTURBATIONS [PDF]
Научно-технический вестник информационных технологий, механики и оптики, 2019 We consider the motion of a mechanical system with several degrees of freedom near zero of the phase space of states under conditions of constantly acting small perturbations. The generalized forces are represented in the dynamic equations by homogeneous
V. G. Melnikov +3 more
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On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems [PDF]
Mathematica Bohemica, 2023 We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center.
Aziza Berbache
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Parameterization of kernels of the Volterra series for systems given by nonlinear differential equations [PDF]
E3S Web of Conferences, 2023 The presented article is devoted on an issue regarding to the transformation of nonlinear models of a certain class to the Volterra functional series. The new identification method based on analytical input and output of a system was developed.
Kislovskiy Evgeniy +2 more
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Quadratic planar differential systems with algebraic limit cycles via quadratic plane Cremona maps
Advances in Mathematics, 2021 In this paper we show how we can transform quadratic systems into new quadratic systems after some kind of birational transformations, the quadratic plane Cremona maps. We afterwards apply these transformations to the families of quadratic differential systems having an algebraic limit cycle.
Alberich Carramiñana, Maria +2 more
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Results in Control and Optimization, 2023 A new method for finding a suboptimal control law for a multi fractional spring–mass system as a fractional high order linear quadratic regulator system in the presence of known disturbance is introduced.
Iman Malmir
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UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS [PDF]
IFAC Proceedings Volumes, 2002 Abstract This paper considers uncertain systems from a behavioural point of view defined via quadratic differential forms. This uncertainty definition is closely related to the integral quadratic constraint uncertainty description commonly found in robust control theory.
Ian R. Petersen, Jan C. Willems
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Linear-Quadratic $N$-person and Mean-Field Games with Ergodic Cost [PDF]
, 2014 We consider stochastic differential games with $N$ players, linear-Gaussian dynamics in arbitrary state-space dimension, and long-time-average cost with quadratic running cost. Admissible controls are feedbacks for which the system is ergodic.
Bardi, Martino, Priuli, Fabio S.
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Exactly Solvable Quadratic Differential Equation Systems Through Generalized Inversion
Qualitative Theory of Dynamical Systems, 2023 AbstractWe study the autonomous systems of quadratic differential equations of the form $${\dot{x}}_i(t)={\textbf{x}}(t)^T {\textbf{A}}_i {\textbf{x}}(t) + {\textbf{v}}_i^T {\textbf{x}}(t)$$ x ˙ i
Bácsi, Ádám, Kocsis, Albert Tihamér
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The Sine-Cosine Wavelet and Its Application in the Optimal Control of Nonlinear Systems with Constraint [PDF]
Journal of Electrical and Computer Engineering Innovations, 2013 In this paper, an optimal control of quadratic performance index with nonlinear constrained is presented. The sine-cosine wavelet operational matrix of integration and product matrix are introduced and applied to reduce nonlinear differential equations ...
R. Hajmohammadi +2 more
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