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Direct energy methods have been extensively developed for the transient stability analysis and contingency screening of power grids. However, there is no analytical energy functions proposed for power grids with losses, which are normal in practice. This paper applies the recently introduced Lyapunov Functions Family approach to the certification of synchronization stability for lossy power grids...
Continuous-time reset control is a hybrid feedback control of a continuous-time controller and a state dependent reset rule. In this paper, a synthesis of the purely output-feedback linear reset control is considered via LMI approach. The reset control consists of the continuous-time controller and the reset law determined by jump and reset matrices. Different from the state-feedback case in the author's...
The paper presents a new explicit and non-redundant parametrization of all state-derivative feedbacks assigning the required Jordan form to the dynamic matrix of the closed loop system. The proposed parametrization can be simply and effectively used for both numerical and symbolic calculations of the state-derivative feedbacks, and also for robust stability and robust performance optimizing.
This paper presents the design of a robust discrete-time sliding mode repetitive controller (DSMRC) which combines the features of repetitive control (RC) and sliding mode control (SMC) to achieve fast transient response, improved robustness to various matched uncertainties, and improved steady state performance. The new control structure consists of a repetitive control component and a sliding mode...
A novel approach to robust controller design with input hard constraints is presented. The proposed design procedure contains robust stability condition based on the M-delta structure and it is used for system with additive uncertainty. The obtained results, illustrated on example, show the applicability of the designed robust controller and its ability to cope with model uncertainties.
In this paper we deal with the analysis of Category II (nonlinear) Pilot in the Loop Oscillations (PIO). They are originated by a misadaptation between the pilot and the aircraft during some tasks in which tight closed loop control of the aircraft is required from the pilot, with the aircraft not responding to pilot commands as expected by the pilot himself. We propose a novel approach, based on robust...
Fuzzy functions are used for the modelling and analysis of systems with variable parametric uncertainty. The approach consists of interpreting a fuzzy number as a family of intervals bounding the parameter space, parameterized by the degree of confidence (reliability) in the model. The uncertainty associated with a fuzzy function with non-fuzzy arguments lies in its parameters, which are fuzzy numbers...
The problem of bounded disturbance rejection for linear impulsive systems with polytopic uncertainties is considered in this paper. By using the Lyapunov function and positively invariant set method, a sufficient condition for robustly internal stability and L1-performance of the impulsive systems is obtained in terms of linear matrix inequalities. A simple algebraic approach to the design of a linear...
This paper focuses on the stability analysis of some nonlinear delay models of a congestion control scheme. Some uncertainty interpretations of the nonlinear terms are proposed and a complete Lyapunov-Krasovskii functional is used for deriving local asymptotic stability conditions in both constant and time-varying delay cases.
Most of the existent linear matrix inequality based conditions for robust stability of time-delay systems in polytopic domains are expressed in terms of constant Lyapunov-Krasovskii functions. This note presents a simple way to extend these conditions in order to construct parameter-dependent functions that provide less conservative results, in both delay-independent and delay-dependent situations.
A simple necessary condition and sufficient condition for robust Hurwitz stability of interval polynomial is obtained using the results of Nie [13] for fixed polynomials. These conditions provide a simple and quick test to detect many unstable systems. Furthermore, these conditions are used to derive a robust controller for interval plants which involves less computational complexity compared to extreme...
A Matlab toolbox implemented for the computation of the stability margin of uncertain systems affected by structured perturbations is presented. The linear time-invariant systems that can be considered depend on continuously and nonlinearly by uncertain parameters. The proposed algorithm computes the stability margin as the maximal l∞ domain in the parameter space compatible with stability. At the...
There is increasing interest in the control of communication networks. This paper reveals that a simple method, the dual-locus diagram method, is very effective in analyzing the robust stability of simple time-delay systems, which are often met in communication systems. As to a single connection studied in [15], the same results as those obtained by Niculescu have been obtained, but in a much simpler...
This paper considers the problem of robust stabilization and disturbance attenuation for a class of uncertain singularly perturbed systems with norm-bounded nonlinear uncertainties. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed-loop system for all ε ∊(0,∞). Based on this key result and some standard Riccati inequality approaches for robust...
Robust stability conditions for Networked Controlled Systems (NCS) with uncertain, varying, bounded transmission delays and discrete-time static control laws are derived in this article. The delay uncertainty is shown to give rise to a discrete-time uncertain NCS model. The robust stability analysis is carried out via a linear matrix inequality approach which, when combined with a directed parameter...
This paper analyzes the amplitude dependent behavior of nonlinear sampled-data control systems in a frequency domain. We apply the robust stability condition for nonlinear discrete-time feedback systems (which was derived in our previous papers) to a sampled-data control system containing a single nonlinear element in the forward path. In addition, we derive an instability condition for that type...
This paper investigates the robust stability of uncertain linear time-varying systems with a mode-switch dynamics. Each mode is characterized by a dynamical matrix containing elements whose time behavior over bounded time intervals is described by interval polynomials of arbitrary degree. Using a quadratic Lyapunov function polynomially depending on time, stability conditions for each mode are stated...
The asymptotic stability of positive continuous-time linear systems with delays is addressed. It is shown that: 1) the asymptotic stability of the positive systems with delays is independent of their delays, 2) the checking of the asymptotic stability of the positive systems with delays can be reduced to checking of the asymptotic stability of positive systems without delays. Simple stability conditions...
This paper develops a method to analyse robust stability of a generic electrical power system for safe-critical applications over all operating conditions. Standard methods can guaranty stability under nominal conditions but do not take into account any uncertainties of the model. In this work, stability is assessed by using a Structural Singular Value concept that can provide a measure of stability...
This note considers the work entitled “Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0<\alpha<1$ Case” by Lu and Chen, where the authors meant to provide sufficient and necessary conditions for stability of fractional-order linear-time-invariant interval systems. As this note proves, conditions are only sufficient, since necessity...
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