Partial Pole Placement via Delay Action: A Python Software for Delayed Feedback Stabilizing Design

Stabilization by Means of Approximate Predictors for Systems with Delayed Input

Sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented. An approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay. A systematic procedure for the construction of approximate predictors is provided for globally Lipschitz systems. The resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law. Illustrating examples show the efficiency of the proposed control strategy.

New Features of P3$δ$ software: Partial Pole Placement via Delay Action

This paper presents the software Partial Pole Placement via Delay Action, or P3$δ$ for short. P3$δ$ is a Python software with a friendly user interface for the design of parametric stabilizing feedback laws with time-delays, thanks to two properties of the distribution of quasipolynomials' zeros, called multiplicity-induced-dominancy and coexisting real roots-induced-dominancy. After recalling recent theoretical results on these properties and their use for the feedback stabilization of control systems operating under time delays, the paper presents the main features of the current version of …

On Placement of Synthetic Inertia with Explicit Time-Domain Constraints

Rotational inertia is stabilizing the frequency of electric power systems against small and large disturbances, but it is also the cause for oscillations between generators. As more and more conventional generators are replaced by renewable generation with little or no inertia, the dynamics of power systems will change. It has been proposed to add synthetic inertia to the power system to counteract these changes. This paper presents an algorithm to compute the optimal placement of synthetic inertia and damping in the system with respect to explicit time-domain constraints on the rate of change…

On the stability of cycles by delayed feedback control

We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing $T$-cycles of a differentiable function $f: \mathbb{R}\rightarrow\mathbb{R}$ of the form $$x(k+1) = f(x(k)) + u(k)$$ where $$u(k) = (a_1 - 1)f(x(k)) + a_2 f(x(k-T)) + ... + a_N f(x(k-(N-1)T))\;,$$ with $a_1 + ... + a_N = 1$. Following an approach of Morgül, we construct a map $F: \mathbb{R}^{T+1} \rightarrow \mathbb{R}^{T+1}$ whose fixed points correspond to $T$-cycles of $f$. We then analyze the local stabi…

New Features of P3$δ$ Software. Insights and Demos

This paper presents the software entitled "Partial Pole Placement via Delay Action", or "P3$δ$" for short. P3$δ$ is a Python software with a friendly user interface for the design of parametric stabilizing feedback laws with time-delays for dynamical systems. After recalling the theoretical foundation of the so-called "Partial Pole Placement" methodology we propose as well the main features of the current version of P3$δ$. We illustrate its use in feedback stabilization of several control systems operating under time delays.

具有时间延迟动态输入扰动的三角系统全局稳定化

Global Stabilization of Triangular Systems with Time-Delayed Dynamic Input Perturbations

本文提出了一种针对具有时间延迟动态不确定输入非线性的严格反馈类非线性系统的设计方法，通过双动态高增益缩放结构设计全局稳定延迟无关鲁棒自适应输出反馈控制器。