Robust Stability Analysis Research Articles

Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays

This paper investigates the delay-dependent robust stability problem of fuzzy stochastic Hopfield neural networks with random timevarying delays. Moreover, in this paper, the stochastic delay is assumed to satisfy a certain probability distribution. By introducing a stochastic variable with Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. Based on a LyapunovKrasovskii functional and stochastic analysis approach, delay-probability-distribution-dependent stability criteria have been derived in terms of linear matrix inequalities (LMIs), which can be checked easily by the LMI control toolbox. Finally two numerical examples are given to illustrate the effectiveness of the theoretical results.

A robust stochastic stability analysis approach for power system considering wind speed prediction error based on Markov model

This paper proposes a robust stochastic stability analysis approach with partly unknown transition probability by considering the wind speed prediction error in power system. Firstly, taking this prediction error into account, based on Markov modeling theory, the stochastic dynamic model of wind power system with uncertain transition probability is developed. Secondly, according to the stochastic stability theory of Markov jump system, the transition probability of wind power system mode is divided into three cases: fully known, only known upper and lower bounds, and completely unknown. Then, by using linear matrix inequality (LMI) technology, a robust stochastic stability criterion with disturbance attenuation is obtained. Finally, test results show that the proposed analysis approach does not need to obtain the trajectory of the actual system operation parameters, and has the advantages of high computational efficiency.

Robust Adaptive Stabilization by Delay Under State Parametric Uncertainty and Measurement Bias

An output robust adaptive control is designed for a class of Lipschitz nonlinear systems under assumption that the measurements are available with a constant bias and the state equations linearly parameterized by unknown parameters and external disturbances. A dynamic state reconstruction (synthesis of an observer) is avoided by using delayed values of the output in the feedback and adaptation laws. The analysis of robust stability for the resulted time-delay system is performed by using the Lyapunov–Krasovskii approach. The control and adaptation gains can be selected as a solution of the proposed linear matrix inequalities. This research is motivated by a nonlinear pendulum control problem, and the efficacy of the developed control is demonstrated on this application through experiments.

Novel Robust Stability Criteria of Uncertain Systems with Interval Time-Varying Delay Based on Time-Delay Segmentation Method and Multiple Integrals Functional

Interval time-varying delay is common in control process, e.g., automatic robot control system, and its stability analysis is of great significance to ensure the reliable control of industrial processes. In order to improve the conservation of the existing robust stability analysis method, this paper considers a class of linear systems with norm-bounded uncertainty and interval time-varying delay as the research object. Less conservative robust stability criterion is put forward based on augmented Lyapunov-Krasovskii (L-K) functional method and reciprocally convex combination. Firstly, the delay interval is partitioned into multiple equidistant subintervals, and a new Lyapunov-Krasovskii functional comprising quadruple-integral term is introduced for each subinterval. Secondly, a novel delay-dependent stability criterion in terms of linear matrix inequalities (LMIs) is given by less conservative Wirtinger-based integral inequality approach. Three numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion. For the first example about closed-loop control systems with interval time-varying delays, the proposed robust stability criterion could get MADB (Maximum Allowable Delay Bound) about 0.3 more than the best results in the previous literature; and, for two other uncertain systems with interval time-varying delays, the MADB results obtained by the proposed method are better than those in the previous literature by about 0.045 and 0.054, respectively. All the example results obtained in this paper clearly show that our approach is better than other existing methods.

Robust Stability Analysis of Delayed Stochastic Neural Networks via Wirtinger-Based Integral Inequality.

We discuss stability analysis for uncertain stochastic neural networks (SNNs) with time delay in this letter. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and utilizing Wirtinger inequalities for estimating the integral inequalities, the delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs). We discuss the parameter uncertainties in terms of norm-bounded conditions in the given interval with constant delay. The derived conditions ensure that the global, asymptotic stability of the states for the proposed SNNs. We verify the effectiveness and applicability of the proposed criteria with numerical examples.

Robust Control and Stability Analysis of Computerized Numeric Controlled Machine Tool under Parametric Uncertainty

The objective of this paper is to design three different robust controllers such as proportional-integral (PI), internal model control (IMC), and H∞ control techniques for position control of the computerized numeric controlled machine tool (CNCMT) system. The proposed controllers aim to control the servo motor that regulates the position of the machine table and also enhances the robustness of the CNCMT system under the influence of parametric uncertainties. The stability of the uncertain CNCMT system with all designed controllers is investigated using Kharitonov’s theorem. The stability margin (SM) criterion is utilized for robustness analysis.

Robust stability analysis of uncertain incommensurate fractional order quasi-polynomials in the presence of interval fractional orders and interval coefficients

This paper deals with the robust stability analysis of a class of incommensurate fractional order quasi-polynomials with a general type of interval uncertainties. The concept of the general type of interval uncertainties means that all the coefficients and orders of the fractional order quasi-polynomials have interval uncertainties. Generally, the computational complexity of specifying the robust stability of such a quasi-polynomial is shown in this paper. To this end, the robust stability is studied by Principle of Argument theorem. In fact, by presenting two theorems and three lemmas it is shown that the robust stability of a fractional order quasi-polynomial involving the general type of uncertainty can be simply investigated without needing to plot its value set by heavy computations. Examples are attested the validity of the paper results.

The optimal detuning approach based centralized control design for MIMO processes

This manuscript introduces an optimal detuning approach for designing a centralized PI control system for multi-input multi-output (MIMO) processes. Based on the approach, two multivariable PI controller designs are proposed in this manuscript. The proposed approach formulates the centralized PI controller design problem in an optimization framework and transforms it into an equivalent detuning parameter(s) design problem. While the centralized controller design with the proposed 1-Optimal Detuning Parameter (ODP) method is carried out as a multi-stage problem, the proposed 2-ODP method formulates the controller design as a single-stage optimization problem. An effective transfer function (ETF) parameterization followed by controller synthesis using the IMC theory and further the optimal detuning comprises the various stages in 1-ODP design. In this regard, a novel ETF parameterization procedure for large scale processes or systems with higher-order elements is presented in this manuscript. Contrary to the centralized controller design in the kp,ki space, where the dimensionality of the optimization problem blows at O(2n2), the proposed 1-ODP and 2-ODP design methods always aim at solving a uni- and bi-dimensional optimization problem, respectively, irrespective of the dimensionality of the MIMO process. Hence, the proposed method is easily applicable even to high-dimensional MIMO processes. Several illustrative industrial MIMO systems are considered to demonstrate the applicability of the proposed methods to highly interacting and large scale processes. The simulation studies show that the proposed methods performs better as compared to the other centralized PI controller designs. Even with parameter variations, the proposed methods give satisfactory closed-loop performance. Further, robust stability analysis for the proposed designs is performed by considering multiplicative input and output uncertainties.

Determination of vertex polynomials to analyse robust stability of control systems with interval parameters

The study describes the application of the root locus theory for a system whose characteristic polynomial has interval coefficients. For the proposed system, an interval extension of the basic angular equation of the root locus is performed. Upon the conditions for defining the robust oscillatory stability degree through a complex pole of the system, the double interval angular inequations are obtained. These inequations specify the range of the exit angles going out of the poles for all edge branches of the root locus. On the basis of the exit angles of edge branches going out of the real pole, the condition for determining the robust aperiodic stability degree is obtained. Moreover, an algorithm for finding the validation vertices of the polyhedron of coefficients is developed and some sets of vertex polynomials for low-order systems are specified. The study also presents some numerical examples for analysing the robust stability degree in interval systems, which confirm our theoretical results. It is concluded that the determined validation vertices provide an optimal solution to the analysis of robust stability.

Robust stability analysis of interval fractional-order plants by fractional-order controllers: an approach to reduce additional calculation

This paper investigates the robust stability of fractional-order plants suffering from interval uncertainties by using fractional-order controllers. Based on the zero-exclusion principle, at first, new necessary and sufficient criteria are proposed to analyze the robust stability of the corresponding characteristic polynomial. Then, an auxiliary function is presented to investigate the robust stability criteria. The results of this paper also help to reduce additional calculations noticeably since the vertices used in the auxiliary function are fixed for all positive frequencies. Finally, three numerical examples are given to indicate the effectiveness of the paper results.

Robust stability analysis of uncertain fractional order neutral-type delay nonlinear systems with actuator saturation

In this paper, we study the robust stability of uncertain fractional order (FO) nonlinear systems having neutral-type delay and input saturation. From the Lyapunov–Krasovskii functional, sufficient criteria on asymptotic robust stability of such FO systems with the help of linear matrix inequalities are specified to compute the gain of state-feedback controller. An optimization is also derived using the cone complementarity linearization method for finding the controller gains subject to maximizing the domain of attraction. The main results are confirmed via numerical examples.

Robust stability analysis of incommensurate fractional-order systems with time-varying interval uncertainties

This paper focuses on the stability analysis of the incommensurate fractional-order systems describing by the pseudo-state-space form in the presence of interval uncertainties. By using the generalized small-gain theorem and the properties of M-matrices, a condition is achieved for robust finite-gain L2 stability of these systems. In addition, satisfying this condition ensures the asymptotic stability of uncertain fractional-order systems, based on the Caputo definition. Unlike the methods which are based on the eigenvalue argument checking, the proposed robust stability analysis method can be used for systems with irrational fractional orders and time-varying uncertainties. Compared with the Lyapunov based methods, the conservatism due to the lack of relation between stability condition and fractional-order of the system does not occur in the proposed method. An illustrative example is presented to confirm this method does not lead to conservatism generated by reformulation of the interval uncertainty, which is the basis of the commonly used methods in the literature. Finally, the suggested method is employed for robust stability checking of the Sallen–Key filter including fractional capacitors with irrational orders.

Advanced aeroelastic robust stability analysis with structural uncertainties

Robust flutter analysis described in this paper is based on the robust control theory framework. Therefore, a time-domain linear fractional transformation representation of the perturbed aeroelastic system is modeled. Then, the robust stability is analyzed by means of the structured singular value mu, which is defined as an alternative measure of robustness. Robust flutter analysis deals with aeroelastic (or aeroservoelastic) stability analysis taking structural dynamics, aerodynamics and/or unmodeled system dynamics uncertainties into account. Flutter is a well-known dynamic aeroelastic instability phenomenon caused by an interaction between structural vibrations and unsteady aerodynamic forces, whereby the level of vibration may trigger large amplitudes, eventually leading to catastrophic failure of the structure. The primary motivation of the robust flutter analysis is that this method allows the computation of the worst-case flutter velocity which can support, for example, the flight test program by a valuable robust flutter boundary. This paper addresses the issue of an approach for aeroelastic robust stability analysis with structural uncertainties with respect to physical symmetric and asymmetric stiffness perturbations on the wing structure by means of tuning beams.

Robust stability analysis for linear systems with distributed delays: A time‐domain approach

SummaryThis work is devoted to the robust stability analysis of linear systems with distributed delays. The approach is based on recent results in the Lyapunov‐Krasovskii framework, where a Lyapunov‐Krasovskii functional with prescribed negative definite derivative is applied. The stability conditions obtained in this work, are simple inequalities which depend on the so‐called delay Lyapunov matrix. The cases of matrix parameters and delays uncertainties are addressed, accurately detecting exact stability bounds when applied in an iterative manner. Our method is used successfully to tackle the challenging problem of robust predictor‐based stabilization of systems with state and input delays.

Robust stability analysis for feedback systems with simultaneous uncertainties via IQCs

The robust stability of feedback interconnections is studied for a class of continuous-time causal linear systems over finite-energy signals of non-uniformly lower-bounded support. The stability of the feedback system with simultaneous uncertainties in the plant and the controller is exploited via integral quadratic constraints (IQCs), in which the plants and controllers are taken from two path-connected uncertainty sets with respect to the Feintuch's time-varying gap metric. Subsequently, the robust stability of the two-port networked system is characterised by means of the combination of IQCs and the time-varying gap. In particular, some robust stability criteria are applicable to the linear systems that do not have strong graph representations.

Model based control strategies to control voltage of Proton Exchange Membrane Fuel Cell

Abstract The present work deals with the evaluation of model based control strategies for a PEM fuel cell to control voltage. PEM fuel cell is an electrochemical device that converts the chemical energy to electrical energy. Stack voltage is affected by many factors like stack temperature, moisture content of the membrane, partial pressure of hydrogen and air, inlet rate of hydrogen and air and also fuel starvation affects the rate of reaction and hence the voltage produced. In this work, two single input single output models are taken with stack voltage as controlled variable and hydrogen and air flow rate as manipulated variables respectively. The simulation study on two different control structures i.e., feedback and feedback plus feed forward control structures evaluates the effectiveness of proposed controllers concerning set-point tracking and disturbance rejection. Comparative study is carried out by simulations by implementing various model based control strategies, PI, IMC-PID and MPC. The results shows that MPC gives best results in terms of Integral Square error (ISE), Integral Absolute error (IAE) and controller effort (TV). In addition, robust stability analysis is carried out for uncertainty in the process parameters. Also, the controller fragility is studied for uncertainty in the controller parameters.

Guardian maps based robust stability analysis with applications in flight control of hypersonic vehicles

Guardian maps provide a concise and practical approach to parametric robustness analysis. However, non-convexity and nonlinearity of high dimensional guardian maps restrict the application. In this paper, a closed-loop performance-oriented approach to parametric robustness analysis is proposed. First, a sufficient condition for the existence of parametric stable region satisfying the closed-loop performance is presented. To further identify the maximum stable region, a robustness criterion is provided, leading to a numerical approach for parametric stability margin. The superiority of the proposed method lies in the applicability to robust performance analysis with nonlinear high-dimensional parameters. Applications are discussed with emphasis on the flight control of hypersonic vehicles, including robust control design and robust stability analysis. Results are of significant that no prior knowledge on controller tuning is required, and parametric stability margin can be obtained automatically regardless of the dimension of parameter space.

Robust stability of fractional-order quaternion-valued neural networks with neutral delays and parameter uncertainties

This paper focuses on the robust stability analysis of fractional-order quaternion-valued neural networks (FOQVNNs) with neutral delay and parameter uncertainties. Without transforming the FOQVNNs into equivalent two complex-valued systems or four real-valued systems, based on homeomorphism principle, matrix inequality technique and Lyapunov method, both delay-independent and delay-dependent criteria to guarantee the existence, uniqueness and global stability of equilibrium point for the considered FOQVNNs are derived in the form of linear matrix inequality (LMI). Two examples with simulations are provided to manifest the theoretical results.

Sliding mode tracking control using finite‐time differentiator in high‐orders nonlinear systems with output stochastic signals

SummaryThis article presents sliding mode tracking control using finite‐time nonlinear differentiator (FND) to the high‐orders nonlinear systems that states are unknown and the output measurement signals involves stochastic disturbances. The FND using singular perturbation technique is applied to estimate the unknown states in the tracking system, and not rely on the model information under the condition of output stochastic signals. The stochastic noises involved in the output measurement signals are restrained sufficiently by the FNDs. The design of sliding mode tracking controller using FND reduces the chattering phenomenon efficiently. The analysis of systems stability and differentiator robustness is demonstrated. The comparative simulation results show that the sliding mode controller using FND track the desired trajectory in high accuracy with tracking errors fast convergence.

Receptance-based robust stability criteria for second-order linear systems with time-varying delay and unstructured uncertainties

This paper presents new frequency domain criteria for the robust stability analysis of closed-loop second-order systems under time-varying internal delay. The proposed approach is derived from the small gain theorem for systems described by the versatile system receptance to guarantee robust stability despite time-varying delays and model uncertainties. Robust stability of systems with time-varying delays is challenging to cope because time-invariant paradigm does not hold, but the proposed approach is directly based on the frequency response analysis of the closed-loop system with unstructured uncertainty bound. The criteria can be applied to either single or multiple inputs systems, and no constraint is imposed on the delay derivative. A simple receptance-based Internal Model Control strategy is proposed to improve robust stability margins while nominal state-feedback design is preserved. Thus, a controller obtained from the delay-free nominal model can be used to ensure the robust stability of the uncertain second-order system with time-varying delay. Simulation case studies are used to illustrate the benefits of the proposed criteria.