arXiv subjects

Anton Ponomarev

Publications and source records attributed to Anton Ponomarev.

7 recordsLinked to original sources

arXiv2026

Compositional small-gain and small-phase stability analysis

We adapt the small-gain and small-phase stability analysis to systems composed of MIMO LTI subsystems via an iteration of the series, parallel, and feedback interconnections. Based on a certain set of parameters (including the phase sector and the Crawford number) of the subsystems, we bound the same set of parameters of each consecutive interconnection. This is called "composition of bounds." Composing the gains of subsystems in the same manner enables the small-gain-or-phase analysis of fairly complex systems. The method is illustrated with two examples that are not tractable by the classical small-phase analysis, and one other example that nevertheless benefits from the compositional approach.

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arXiv2026

Period-aware asymptotic gain with application to a periodically forced synchronization circuit

The classical asymptotic gain (AG) is a concept known from the input-to-state stability theory. Given a uniform input bound, AG estimates the asymptotic bound of the output. Sometimes, however, more information is known about the input than just a bound. In this paper we consider the case of a periodic input. Under the assumption that the system converges to a periodic solution, we introduce a new gain, called period-aware asymptotic gain (PAG), which employs periodicity to enable a sharper asymptotic estimation of the output. Since the PAG can distinguish between short-period ("high-frequency") and long-period ("low-frequency") signals, it is able to rigorously quantify such properties as bandwidth, resonant behavior, and high-frequency damping. We discuss how the PAG can be computed and illustrate it with a numerical example from the field of power electronics.

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arXiv2025

Numerical estimation of the lock-in domain of a DC/AC inverter

We estimate the lock-in domain of the origin of a current control system which is used in common DC/AC inverter designs. The system is a cascade connection of a 4-dimensional linear system (current controller, CC) followed by a two-dimensional nonlinear system (phase-locked loop, PLL). For the PLL, we construct a Lyapunov function via numerical approximation of its level curves. In combination with the quadratic Lyapunov function of the CC, it forms a vector Lyapunov function (VLF) for the overall system. A forward-invariant set of the VLF is found via numerical application of the comparison principle. By LaSalle's invariance principle, convergence to the origin is established.

math.OC↗

arXiv2025

Stability of two-dimensional SISO LTI system with bounded feedback gain that has bounded derivative

We consider a two-dimensional SISO LTI system closed by uncertain linear feedback. The feedback gain is time-varying, bounded, and has a bounded derivative (both bounds are known). We investigate the asymptotic stability of this system under all admissible behaviors of the gain. Note that the situation is similar to the classical absolute stability problem of Lurie--Aizerman with two differences: linearity and derivative constraint. Our method of analysis is therefore inspired by the variational ideas of Pyatnitskii, Barabanov, Margaliot, and others developed for the absolute stability problem. We derive the Hamilton--Jacobi--Bellman equation for a function describing the "most unstable" of the possible portraits of the closed-loop system. A numerical method is proposed for solving the equation. Based on the solution, sufficient conditions are formulated for the asymptotic stability and instability. The method is applied to an equation arising from the analysis of a power electronics synchronization circuit.

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arXiv2020

Characteristics-based Simulink implementation of first-order quasilinear partial differential equations

The paper deals with solving first-order quasilinear partial differential equations in an online simulation environment, such as Simulink, utilizing the well-known and well-recommended method of characteristics. Compared to the commonly applied space discretization methods on static grids, the characteristics-based approach provides better numerical stability. Simulink subsystem implementing the method of characteristics is developed. It employs Simulink's built-in solver and its zero-crossing detection algorithm to perform simultaneous integration of a pool of characteristics as well as to create new characteristics dynamically and discard the old ones. Numerical accuracy of the solution thus obtained is established. The subsystem has been tested on a full-state feedback example and produced better results than the space discretization-based "method of lines". The implementation is available for download and can be used in a wide range of models.

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arXiv2016

Nonlinear Predictor Feedback for Input-Affine Systems with Distributed Input Delays

Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero. Stabilization of the new system leads to Lyapunov-Krasovskii proven stabilization of the original one. Conditions on the original system are: smooth linearly bounded open-loop vector field and smooth uniformly bounded input vectors. About the transformed system which turns out to be affine in the undelayed input but with input vectors dependent on the input history and system state, we assume existence of a linearly bounded stabilizing feedback and quadratically bounded control-Lyapunov function. If all assumptions hold globally, then achieved exponential stability is global, otherwise local. Analytical and numerical control design examples are provided.

math.OC↗

arXiv2015

Reduction-Based Robustness Analysis of Linear Predictor Feedback for Distributed Input Delays

Lyapunov-Krasovskii approach is applied to parameter- and delay-robustness analysis of the feedback suggested by Manitius and Olbrot for a linear time-invariant system with distributed input delay. A functional is designed based on Artstein's system reduction technique. It depends on the norms of the reduction-transformed plant state and original actuator state. The functional is used to prove that the feedback is stabilizing when there is a slight mismatch in the system matrices and delay values between the plant and controller.

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