178,094 research outputs found
Conserved- and zero-mean quadratic quantities in oscillatory systems
No full textWe study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities. We also state an equipartition of energy principle for oscillatory systems
Time-relevant stability of 2D systems
No full textFor many 2D systems, one of the independent variables plays a distinct role in the evolution of the trajectories; since often this special independent variable is time, we call such systems 'time-relevant'. In this paper, we introduce a stability notion for time-relevant systems described by higher-order difference equations. We give algebraic tests in terms of the location of the zeros of the determinant of a polynomial matrix describing the system. We also give an LMI characterization of time-relevant stability involving only constant matrices
Identification and data-driven model reduction of state-space representations of lossless and dissipative systems from noise-free data
No full textWe illustrate procedures to identify a state-space representation of a lossless- or dissipative system from a given noise-free trajectory; important special cases are passive- and bounded-real systems. Computing a rank-revealing factorization of a Gramian-like matrix constructed from the data, a state sequence can be obtained; state-space equations are then computed solving a system of linear equations. This idea is also applied to perform model reduction by obtaining a balanced realization directly from data and truncating it to obtain a reduced-order mode
Autonomy, forward non-Zenoness and quadratic stability of bimodal higher-order piecewise linear systems
No full textWe 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
Garuccio-Rapisarda-Vigier Experiment Revisited
No full textWe propose a setup for the experimental implementation of the conceptual experiment proposed, in 1982, by Garuccio, Rapisarda and Vigier. In particular, we show that orthodox quantum mechanics leads to a different prediction with respect to the nonlinear causal approach. Hence, this experiment shall contribute to clarify the ontic nature of quantum wave
Recursive exact H-infinity identification from impulse-response measurements
No full textWe study the H∞-partial realization problem from a behavioral point of view; we give necessary and sufficient conditions for solvability, and a characterization of all solutions. Instrumental in such analysis is the notion of time- and space-symmetrization of the data, which allows to transform the realization problem with metric- and stability constraints into an unconstrained behavioral modeling one
Balanced state-space representations: a polynomial algebraic approach
No full textWe show how to compute a minimal Riccati-balanced state map and a minimal Riccati-balanced state space representation starting from an image representation of a strictly dissipative system. The result is based on an iterative procedure to solve a generalization of the Nevanlinna interpolation problem
Modelling of switching dynamics in electrical systems
No full textIn this paper, we use the switched linear differential systems framework [8] to model electrical devices with switching dynamics. Modularity, i.e. independent modelling and incremental combination of complex dynamics, is an important feature of this approach, since we can incorporate new dynamic modes to the bank without altering the existing ones. This makes our approach ideal for describing complex systems (e.g. energy distribution networks). Our modelling approach differs fundamentally from the traditional representation-based theory where the use of a global state space is required
Stabilization, Lyapunov functions, and dissipation
No full textFor linear time-invariant systems any stabilizing controller for a given plant can be associated with a supply rate with respect to which the plant in open-loop is half-line dissipative. We also prove the equivalence between stability of the interconnection of two systems and their half-line dissipativity with respect to a supply rate and its negative
A two-variable approach to solve the polynomial Lyapunov equation
No full textA two-variable polynomial approach to solve the one-variable polynomial Lyapunov equation is proposed. Lifting the problem from the one-variable to the two-variable context allows to use Faddeev-type recursions in order to solve the polynomial Lyapunov equation in an iterative fashion. The method is especially suitable for applications requiring exact or symbolic computation
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