Robust Stability Analysis Research Articles

Robust Stability Analysis for Linear Systems with Uncertain Fast-Varying Time Delay arising from Networked Control Systems

Robust Stability Analysis for Linear Systems with Uncertain Fast-Varying Time Delay arising from Networked Control Systems

Robust PID control of power in lead cooled fast reactors: A direct synthesis framework

Output core power control for an innovative design of lead cooled fast reactors (BREST) is investigated applying a PID design approach. The reactor core model is developed through a lumped parameter thermo-neutronic coupled layout of the plant. Control design is carried out within a direct synthesis framework whereby desired closed loop characteristics are incorporated. The PID coefficients are calculated employing a Laurent expansion of the intended controller and the resultant control scheme is employed on the uncertain nonlinear reactor plant. A worst case robust stability analysis is thereby conducted for the extreme hypothetical working point of the reactor subject to a near prompt criticality reactivity insertion. Results confirm that the control practice proposed may quite satisfactorily be implemented on the original plant as reasonable robustness characteristics are preserved for this ultimate operational point of the system. Nyquist stability criterion has been resorted for robust stability analysis with cycle burnup reactivity swing taken as the source of uncertainty and further recast into a multiplicative layout. The overall control method for desired power trajectories provides a safe reactivity insertion rate and a feasible rod speed.

Robust stability of fractional order system with general interval uncertainties

This paper focuses on the analysis of robust stability of fractional order system with general interval uncertainties. The concept of general interval uncertainties means that the interval uncertainties exist both in the coefficients and orders of the fractional order system. Necessary and sufficient conditions are proposed to check the robust stability of general interval fractional order system. According to the proposed stability criterion, it is interesting to find that the Edge Theorem, which was initially proposed for integer order system, cannot be directly extended to test the stability of fractional order system with general interval uncertainties. Examples are followed to verify the validity of the proposed method.

Robust stability analysis for uncertain recurrent neural networks with leakage delay based on delay-partitioning approach

This paper focuses on the issue of robust stability analysis for recurrent neural networks (RNNs) with leakage delay. By constructing a novel Lyapunov–Krasovskii functional together with the reciprocally convex approach and the free-weighting matrix technique, some less conservative stability criteria in terms of linear matrix inequalities for RNNs are derived. The new contribution of this paper is that a novel delay-partitioning method is proposed, and some new zero equalities are introduced. Finally, several examples are given to demonstrate the effectiveness of the proposed methods. The simulated results reveal that the leakage delay has great influence on the dynamical systems, and it cannot be neglected.

Robust learning in SpikeProp

Training a Spiking Neural Network using SpikeProp and its derivatives faces stability issues. Surges, marked by a sudden rise in learning cost, are a common occurrence during the learning process. They disrupt the learning process and often destabilize the process resulting in failure. A proper learning rate, which is neither too small nor too big, is important to minimize surges. Furthermore, external disturbances due to imperfection in sample data as well as internal disturbances are additional destabilizing source during the learning process. In this paper, we perform error system analysis incorporating external disturbance, followed by weight convergence analysis along with detailed robust stability analysis of SpikeProp learning process to ensure error bound of the learning process. Based on these results, we propose a robust adaptive learning rate scheme that aligns with the results of theoretical analysis. The performance of the proposed method has been compared with other prevalent methods based on different benchmark datasets and the results demonstrate that our method indeed has better performance in terms of convergence and learning speed as well.

PID Predictive Control of Automobile Engine Air-Fuel Rati Based on the Unscented Kalman Filter

In order to overcome the disadvantage that single-degree-of-freedom PID controller cannot integrate the optimal target tracking performance and anti-interference function, this article puts forward a design of two-degree-of-freedom IMC-PID controller for the time-delay control system according to the Internal Model Control (IMC) principle. It also puts forward a parameter setting method for the two-degree-of-freedom controller based on the maximum sensitivity. First of all, it deduces the relationship between one of the filter parameters with the maximum sensitivity, and determine this parameter according to the maximum sensitivity index, which gives the system strong robustness; then it revises another filter parameter according to the dynamic performance of the system, which gives the system a strong target tracking characteristic. Meanwhile, it conducts the robust stability analysis on the process model mismatch condition, and obtains the conditions for system stability. According to the simulation results, the timedelay control system which is designed based on two-degree-of-freedom IMC-PID controller has good target tracking characteristic, anti-interference performance and robustness, which proves that the parameter setting method which is based on the maximum sensitivity is effective. The negative impact of time delay on the system can be effectively overcome by using the method put forward here.

A note on robust stability analysis of fractional order interval systems by minimum argument vertex and edge polynomials

By using power mapping, stability analysis of fractional order polynomials was simplified to the stability analysis of expanded degree integer order polynomials in the first Riemann sheet. However, more investigation is needed for revealing properties of power mapping and demonstration of conformity of Hurwitz stability under power mapping of fractional order characteristic polynomials. Contributions of this study have two folds: Firstly, this paper demonstrates conservation of root argument and magnitude relations under power mapping of characteristic polynomials and thus substantiates validity of Hurwitz stability under power mapping of fractional order characteristic polynomials. This also ensures implications of edge theorem for fractional order interval systems. Secondly, in control engineering point of view, numerical robust stability analysis approaches based on the consideration of minimum argument roots of edge and vertex polynomials are presented. For the computer-aided design of fractional order interval control systems, the minimum argument root principle is applied for a finite set of edge and vertex polynomials, which are sampled from parametric uncertainty box. Several illustrative examples are presented to discuss effectiveness of these approaches.

Adjustable delay interval method based stochastic robust stability analysis of delayed neural networks

The issue of mean-square exponential (MSE) stability of stochastic delayed neural networks (NNs) with parametric uncertainties is considered in this paper. An adjustable delay interval (ADI) method is proposed to construct a novel Lyapunov-Krasovskii functional (LKF). This method relaxes the restriction on fixed upper and lower bounds of the delay intervals. Combining with the generalized Finsler lemma, ADI method leads to a much less conservative delay-dependent stability criterion based on linear matrix inequality (LMI) for concerned system. Some simulations are described to show the usefulness of the proposed approach.

A simple method of tuning parallel cascade controllers for unstable FOPTD systems

A simple method is proposed to design parallel cascade controllers for open loop unstable processes. A proportional (P)controller is considered for the secondary loop and a proportional integral (PI) controller is considered for the primary loop (P/PI control configuration). Coefficients of the corresponding powers of s (Laplace variable), in the numerator is matched with the coefficients of the corresponding powers of s in the denominator of a closed loop transfer function for a servo problem. Three simulation case studies are considered in this paper. The first case involves a stable secondary loop process and an unstable primary process, the second case involves both unstable primary and secondary processes and the third one, a simulation application to a nonlinear bioreactor model equations. For comparison purposes, P/PI controller design is also carried out by improved simultaneous relay autotuning method, synthesis method and minimizing ISE criterion method. It is found that the proposed method gives a better performance. Robust stability analysis using the complimentary sensitivity function is carried out. The present method is found to be more robust.

Nonlinear measure approach for the robust exponential stability analysis of interval inertial Cohen–Grossberg neural networks

This article is concerned with the existence and robust stability of an equilibrium point that related to interval inertial Cohen–Grossberg neural networks. Such condition requires the existence of an equilibrium point to a given system, so the existence and uniqueness of the equilibrium point are emerged via nonlinear measure method. Furthermore, with the help of Halanay inequality lemma, differential mean value theorem as well as inequality technique, several sufficient criteria are derived to ascertain the robust stability of the equilibrium point for the addressed system. The results obtained in this article will be shown to be new and they can be considered alternative results to previously results. Finally, the effectiveness and computational issues of the two models for the analysis are discussed by two examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 459–469, 2016

Synthesis of Distributed Robust H-Infinity Controllers for Interconnected Discrete Time Systems

This paper presents an algorithm for the synthesis of robust distributed controllers for interconnected linear discrete-time systems. For a network of interconnected uncertain linear time-invariant systems, the distributed controller achieves robust stability and a guaranteed level of robust performance in a well-defined H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> sense. The setting of this paper is in discrete time. Based on the theory of dissipative dynamical systems, conditions for the analysis of robust stability and robust performance of networks are derived in terms of feasibility tests of linear matrix inequalities. From these conditions, computationally tractable synthesis conditions are derived. An iterative D-K type of synthesis algorithm is proposed that yields a robust distributed controller. Convergence properties of the algorithm are inferred.

A Modeling Methodology for Robust Stability Analysis of Nonlinear Electrical Power Systems Under Parameter Uncertainties

This paper develops a modeling method for robust stability analysis of nonlinear electrical power systems over a range of operating points and under parameter uncertainties. Standard methods can guarantee stability under nominal conditions, but do not take into account any uncertainties of the model. In this study, stability is assessed by using structured singular value (SSV) analysis, also known as $\mu$ analysis. This method provides a measure of stability robustness of linear systems against all considered sources of structured uncertainties. The aim of this study is to apply the SSV method for robust small-signal analysis of nonlinear systems over a range of operating points and parameter variations. To that end, a modeling methodology is developed to represent any such system with an equivalent linear model that contains all system variability, in addition to being suitable for $\mu$ analysis. The method employs symbolic linearization around an arbitrary operating point. Furthermore, in order to reduce conservativeness in the stability assessment of the nonlinear system, the approach takes into account dependences of operating points on parameter variations. The methodology is verified through $\mu$ analysis of the equivalent linear model of a 4-kW permanent magnet machine drive, which successfully predicts the destabilizing torque over a range of different operating points and under parameter variations. Further, the predictions from $\mu$ analysis are validated against experimental results.

Robust stability analysis with cycling-based LPTV scaling: part I. Fundamental results on its relationship with lifting-based LPTV scaling

ABSTRACTThis paper is concerned with robust stability analysis of discrete-time linear periodically time-varying (LPTV) systems using the cycling-based LPTV scaling approach. To study the properties of this approach in comparison with the lifting-based LPTV scaling approach, we consider exploiting the framework of representing the associated robust stability conditions with infinite matrices. Since it serves as a common framework for comparing the two different LPTV scaling approaches, it provides us with new insights into the relationship between the cycling-based and lifting-based scaling approaches. In particular, we derive fundamental results that enable us to reduce the comparison, with respect to conservativeness in robust stability analysis, of the two scaling approaches with restricted and tractable classes of separators to a modified comparison of the associated classes of what we call infinite-dimensional separators arising in the above infinite matrix framework.

Robust stability analysis with cycling-based LPTV scaling. Part II: its properties under the use of FIR separators

ABSTRACTThis paper is concerned with robust stability analysis of discrete-time linear periodically time-varying (LPTV) systems using the cycling-based LPTV scaling approach. It consists of applying the separator-type robust stability theorem through the cycling-based treatment of such systems, where this paper aims at revealing fundamental properties of this approach when we confine ourselves to what we call finite impulse response (FIR) separators as a theoretically and numerically very tractable class of separators. Specifically, we clarify such properties of the cycling-based LPTV scaling approach using FIR separators that cannot readily be seen under the treatment of general class of separators. This is accomplished by comparing it with another approach, called lifting-based LPTV scaling using FIR separators, through the framework of representing the associated robust stability conditions with infinite matrices. More precisely, this leads us to clarifying the fundamental relationships between the cycling-based and lifting-based approaches under the use of FIR separators. We also provide a numerical example demonstrating the fundamental relationships clarified in this paper.

Robust stability and stabilisation of Boolean networks with disturbance inputs

ABSTRACTThis paper deals with the problems of robust stability analysis and robust stabilisation control design for Boolean networks with disturbance inputs. The main tool used in this paper is the semi-tensor product of matrices. First, a necessary and sufficient condition is presented for the robust stability of Boolean networks based on the algebraic representation of Boolean networks with disturbance inputs. Second, the concept of one-step robust reachability is defined for Boolean control networks (BCNs) with disturbance inputs, based on which a constructive procedure is proposed for the robust stabilisation control design of BCNs. The study of an illustrative example demonstrates the effectiveness of the obtained new results.

Robust finite time stabilization analysis for uncertain neural networks with leakage delay and probabilistic time-varying delays

This paper investigates the problem of robust finite time stabilization for a uncertain neural networks with leakage delay and probabilistic time-varying delays. By introducing a stochastic variable which satisfies Bernoulli distribution, the information of probabilistic time-varying delay is equivalently transformed into the deterministic time-varying delay with stochastic parameters. The main objective of this paper is to design a memoryless state feedback control such that the resulting proposed system is robustly finite time stable with admissible uncertainties. Based on a suitable Lyapunov–Krasovskii functional, model transformation technique and Wirtinger-based double integral inequality, the general framework is obtained in terms of linear matrix inequalities to determine the finite time stability and to achieve the control design. Finally, three numerical examples are presented to validate the effectiveness and less conservatism of the proposed method.

Permutation matrix based robust stability and stabilization for uncertain discrete-time switched TS fuzzy systems with time-varying delays

This study is concerned with the problems of robust asymptotic stability analysis and stabilization with a state feedback controller for a class of uncertain discrete-time switched TS fuzzy systems with time-varying delays. By utilizing permutation matrix approach, delay-independent sufficient conditions are developed for achieving the mission of reducing conservatism and to break with existing ones which are formulated in terms of linear matrix inequalities (LMIs). Lastly, three numerical examples are employed to show the effectiveness and the reduced conservatism of the proposed results.

Robust Stability Analysis and Synthesis for Uncertain Discrete-Time Networked Control Systems Over Fading Channels

This technical note investigates uncertain discrete-time networked control systems over fading channels. It is assumed that the plant is affected by polytopic uncertainty and is connected to the controller in closed-loop via fading channels which are modeled by multiplicative noise processes. Three contributions are proposed as follows. First, it is shown that robust stability in the mean square sense of the uncertain closed-loop networked control system is equivalent to the existence of a Lyapunov function in a certain class. Second, it is shown that the existence of a Lyapunov function in such a class is equivalent to the feasibility of a set of linear matrix inequalities (LMIs). Third, it is shown that the proposed condition can be exploited for the synthesis of robust controllers ensuring robust stability in the mean square sense of the uncertain closed-loop networked control system.

Basis-dependent and delay-dependent results on robust L1 filtering for networked control systems

Persistent and amplitude-bounded disturbances are nowadays considered for various engineering applications. Whereas the traditional H∞ and L2–L∞ filtering methods under the energy-bounded external disturbances assumption cannot receive good noise suppression effect. To effectively reflect the capability of disturbances suppression, this paper proposes a robust L1 filtering approach for a class of nonlinear networked control systems (NNCSs) described by Takagi–Sugeno (T–S) fuzzy model. According to the analysis of the typical time-delay issue induced by communication network and the parallel distributed compensation (PDC) technique, a fuzzy filtering error system is established. Attention is focused on designing the robust L1 filter that guarantees the fuzzy filtering error system to be asymptotically stable and to have a prescribed L1 noise attenuation level γ with respect to all persistent and amplitude-bounded disturbances. In particular, we concentrate on the delay-dependent case, using a basis-dependent Lyapunov–Krasovskii functional which refers to reducing the conservatism, the peak-to-peak performance criterion is first proposed. The integral inequality method and linear matrix inequality (LMI) technique are adopted during the process of robust L1 stability analysis. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed method.

Robust Stability Analysis and Systematic Design of Single-Input Interval Type-2 Fuzzy Logic Controllers

Recent results on fuzzy control have shown that interval type-2 (IT2) fuzzy logic controllers (FLCs) might achieve better control performance due to the additional degree of freedom provided by the footprint of uncertainty (FOU) in their IT2 fuzzy sets. However, the design and robust stability analysis of the IT2-FLCs are still challenging problems due to their relatively more complex internal structure. In this paper, we will derive the explicitly fuzzy mapping (FM) of a single-input IT2-FLC (SIT2-FLC) to present design methods and investigate its robustness. The analytical information of the IT2-FM will give the opportunity to provide explanations on the roles of the FOU parameters by taking advantage of the well-developed framework of nonlinear control theory. Comparative theoretical explorations will be presented on the differences between the type-1 (T1) FM and IT2-FM to clearly show the role of the FOU on the robust control system performance. It will be proven that the robust stability of the IT2 fuzzy system is guaranteed with the aids of the well-known Popov–Lyapunov method. Moreover, analytical design methods are presented for SIT2-FLCs to generate commonly employed control curves by only tuning the size of the FOUs without a need of an optimization procedure. It will be theoretically shown that the FOU gives the opportunity to the SIT2-FLC to generate commonly employed nonlinear control curves while also providing a certain degree of robustness which cannot be accomplished by its T1 counterpart. The presented results provide theoretical explanations on the role of the FOU on the performance and robustness of the SIT2-FLC.