Robust Stability Of System Research Articles

Robust and resilient stabilization and tracking control for chaotic dynamical systems with uncertainties

In this article, a robust resilient design methodology for stabilization and tracking control for a class of chaotic dynamical systems is proposed. In particular, a resilient quasi-sliding mode control law is formulated to suppress the chaotic behaviour of these dynamical systems, while considering uncertainties in control input. By using Lyapunov stability theory, sufficient conditions are derived in terms of Linear Matrix Inequalities (LMIs) for a more general class of chaotic nonlinear dynamical systems satisfying the Lipschitz continuity condition. The control gains are obtained via LMI technique in the presence of bounded additive uncertainties in control input. Numerical simulations are provided for Chua’s circuit, Lorenz system, and 4D Lu hyper-chaotic system to show the supremacy and effectiveness of the proposed design methodologies.

Robust Stability and Stabilization Conditions for Nonlinear Networked Control Systems With Network-Induced Delay via T–S Fuzzy Model

Robust stability and stabilization problems for a class of discrete-time nonlinear systems are studied in this article. The control signal is transmitted to the nonlinear systems through a lossy communication channel in which time-varying network-induced delay occurs. A Takagi–Sugeno (T–S) fuzzy model is used to represent the nonlinear systems. Using membership function boundary information, a novel membership-function-dependent (MFD) analysis approach is presented. Unlike most previous results, the proposed MFD analysis approach does not need to increase the number of slack variables to reduce conservatism. Combining auxiliary matrices and this approach, we propose some new fuzzy Lyapunov–Krasovskii functionals (FLKFs) that do not require the restrictions of positive definiteness imposed on Lyapunov matrices. Using the FLKF and MFD analysis approach, a sufficient condition in the form of linear matrix inequalities (LMIs) is developed to guarantee the stability of T–S fuzzy time-varying delay systems. Based on the results for stability, less conservative stabilization conditions are also derived. Finally, numerical examples show that less conservative results can be obtained by the proposed approach. The inverted pendulum system with state delay or network-induced delay is also studied to verify the effectiveness of the suggested approach.

System Optimization and Robustness Stability Control for GIS Inspection Robot in Complex Microgrid Networks

GIS (gas-insulated switchgear) is important equipment in the substation system in a complex microgrid network. Due to the long-term service in harsh operation environments, the electrical performance of GIS equipment will be seriously affected. Therefore, the regular maintenance of GIS equipment in the substation system is a routine task so as to ensure the normal operation of the microgrid networks. The traditional method relies on manual labor, where not only with the low operation efficiency but also regarding some maintenance, labors cannot reach the inside of the GIS equipment, which seriously restricted the completion of GIS equipment maintenance operation. Based on the above analysis, a basic configuration of a GIS equipment maintenance robot with smart structure, convenient control, and stable motion characteristic has been proposed in this paper. Through the optimization design of the chassis adsorption system, the GIS inspection robot can achieve hanging and vertical adsorption inside the GIS equipment and some special motion status. In this way, the entire GIS equipment can be inspected without blind spots. Through establishing the mechanical model of the GIS inspection robot under the hanging and vertical motion state, the robustness and stability of the GIS inspection robot in the special status have been analyzed, and the corresponding GIS inspection robot robust stability motion control method has also been proposed. Finally, through the integrated design of mechanical system and hardware and software control system, the GIS inspection robot physical prototype system has been developed and the maintenance operation experiment has been carried out in Hunan Electric Power Company Maintenance Company through simulating the internal GIS equipment. The physical prototype can realize the basic movement and special movement in internal GIS equipment without any blind spots and complete the inspection task of GIS equipment operation; the movement of GIS robot is dexterous and stable in the whole operation process, which has strong robust stability. The research of GIS inspection robot in the complex microgrid networks has important theoretical significance and practical application value for the intelligent operation and maintenance management of substation system in complex microgrid networks.

Robust Stabilization of Stochastic Markovian Jump Systems with Distributed Delays

This paper addresses the robust stabilization problem for a class of stochastic Markovian jump systems with distributed delays. The systems under consideration involve Brownian motion, Markov chains, distributed delays, and parameter uncertainties. By an appropriate Lyapunov–Krasovskii functional, the novel delay-dependent stabilization criterion for the stochastic Markovian jump systems is derived in terms of linear matrix inequalities. When given linear matrix inequalities are feasible, an explicit expression of the desired state feedback controller is given. The designed controller, based on the obtained criterion, ensures asymptotically stable in the mean square sense of the resulting closed-loop system. The convenience of the design is greatly enhanced due to the existence of an adjustable parameter in the controller. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed theory.

Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach

The hybrid fractional-order multi-dimensional (N-D) systems described by Roesser model are introduced in this paper. The N-D systems include discrete-time dimensions and fractional-order continuous-time dimensions with fractional-order 0<αi<1. Firstly, some novel sufficient stability conditions for nominal hybrid fractional-order N-D systems are presented. Then, against interval uncertainties, the sufficient conditions for robust stability and stabilization of hybrid fractional-order N-D systems are derived. All the results are in the form of linear matrix inequalities. Finally, illustrative examples are given to verify the validity of our results, and demonstrate that our results are less conservative than the existing ones.

Nonfragile H ∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness.

Development and Validation of RP-HPLC Method for the Simultaneous Estimation of Salbutamol Sulphate and Ambroxol Hydrochloride in Oral Liquid Dosage Form

Pharmaceutical analysis is imported branch of science deals with to check the identity, strength, quality and purity of chemical and herbal compounds. Qualitative analysis of drugs and pharmaceutical compounds. Quantitative analysis is of much importance and done by various methods. One of the most accurate and precise methods is spectrophotometry which comprises the measurement of intensity of electromagnetic radiation emitted or absorbed by the compound. Another most popular method of for quantitative analysis is high performance liquid chromatography (HPLC). In the present article a RP-HPLC method was developed for the simultaneous determination of salbutamol sulphate and ambroxol hydrochloride in oral liquid doses form and validation of the developed method. Developed methods include selection of mobile phase, chromatographic method, and wavelength whereas validation involves the system suitability, accuracy, precision, linearity, reproducibility, robustness, specificity and solution stability of the developed method. The result showed that the developed method is the best suited to the simultaneous determination of salbutamol sulphate and ambroxol hydrochloride and validated as per the standards.&#x0D;

Enhanced two-loop model predictive control design for linear uncertain systems

Model predictive controllers (MPC) with the two-loop scheme are successful approaches practically and can be classified into two main categories, tube-based MPC and MPC-based reference governors (RG). In this paper, an enhanced two-loop MPC design is proposed for a pre-stabilized system with the bounded uncertainty subject to the input and state constraints. The proposed method offers less conservatism than the tube-based MPC methods by enlarging the restricted input constraint. Contrary to the MPC-based RGs, the investigated method improves tracking performance of the pre-stabilized system while satisfying the constraints. Additionally, the robust global asymptotic stability of the closed-loop system is guaranteed in a novel procedure with terminal constraint relaxation. Simulation of the proposed method on a servo system shows its effectiveness in comparison to the others.

Observer-Based Adaptive Hybrid Feedback for Robust Global Attitude Stabilization of a Rigid Body

In this article, an observer-based adaptive hybrid attitude controller is presented that overcomes the topological obstructions associated with the global attitude stabilization. This hybrid controller consists of two major parts: an adaptive trimodal hybrid controller to eliminate unwinding phenomenon, and a centrally synergistic potential function. In the adaptive trimodal hybrid controller, the first logic variable selects, which quaternion representation of the desired attitude should be tracked. Furthermore, an adaptive technique is introduced to collaborate with the second logic variable to adapt the hysteresis width. The third logic variable controls the mismatch between the auxiliary dynamical system and the actual attitude. Moreover, an auxiliary dynamical system and a nonlinear angular velocity observer are presented whose outputs are utilized in the proposed feedback control law to attain the necessary damping. Furthermore, a new centrally synergistic potential function is presented to cooperate with the trimodal hybrid controller to overcome the topological obstruction associated with the vector bundle structure. The robust global asymptotic stability of the consequent closed-loop system is guaranteed through a Lyapunov analysis. A comparative analysis in simulations illustrates the effectiveness and superiority of the proposed control scheme.

A new approach based on the discriminant system of polynomial for robust stability and stabilization of two-dimensional systems

In this paper, we present necessary and sufficient stability and robust stability conditions for two-dimensional (2D) systems described by the Fornasini-Marchesini (FM) second model in terms of the discriminant systems of polynomial. This paper simplifies the traditional method of stability into a tractable method by the fractional linear transformation (FLT). More specifically, we reduce the stability analysis to a easy issue whether some polynomials are positive definite. Then we use the same idea to consider the stabilization and robust stabilization issues. Finally, the effectiveness of the proposed results is demonstrated by a practical example and two numerical examples.

Optimal V-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems

Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal robust stabilization approach for closed-loop fractional order proportional integral derivative (FOPID) control systems with interval parametric uncertainty and uncertain time delay. This stabilization approach, which is carried out in a v-plane, relies on the placement of the minimum angle system pole to a predefined target angle within the stability region of the first Riemann sheet. For this purpose, tuning of FOPID controller coefficients was performed to minimize a root angle error that is defined as the squared difference of minimum angle root of interval characteristic polynomials and the desired target angle within the stability region of the v-plane. To solve this optimization problem, a particle swarm optimization (PSO) algorithm was implemented. Findings of the study reveal that tuning of the target angle can also be used to improve the robust control performance of interval uncertain FOPID control systems. Illustrative examples demonstrated the effectiveness of the proposed v-domain, optimal, robust stabilization of FOPID control systems.

Dynamical Analysis and Sampled-Data Stabilization of Memristor-Based Chua’s Circuits

In this paper, we investigate sampled-data stabilization of memristor nonlinearity in Chua's circuits. The system stability pertaining to its switching nonlinearity covers two situations of flux thresholds. Through the stability analysis, the multistability characteristic is proved by its periodic invariant stable line. Moreover, the dynamical features of the considered system are examined in details by numerical and corresponding simulated experiments. Several statistical and analytical characteristic methods are used to confirm the existence of chaotic attractors. With the help of Lyapunov stability theory, new sufficient conditions are formulated using the linear matrix inequality (LMI) method to ensure robust stability and stabilization of closed-loop systems. Finally, we present a numerical example to ascertain the validity of the theoretical results obtained.

Robust Fuzzy Model Predictive Control with time delays for Nonlinear Systems

In this work, a robust fuzzy model predictive control (RFMPC) is designed for uncertain time-delay systems under input constraints with external disturbances. The proposed controller is based on an augmented state space model that includes the state variables and output tracking error variable of system. As a result, the proposed control based on augmented state space model can guarantee the convergence and tracking performance of system. To ensure the stability of the closed loop constrained time-delays system, in the form of linear matrix inequalities (LMIs), the Lyapunov–Krasovskii (L-K) theory is employed to derive sufficient stability conditions where the L-K theory has the ability to reflect the system’s original state space and its advantages in controller synthesis and computation. As a result, less conservative stable conditions in terms of LMIs are given and used to ensure the asymptotically robust stability of closed-loop constrained system, and the controller construction procedure in shifted into a minimization problem subjected to certain constraints in terms of LMI. The robustness properties of the proposed RFMPC approach are compared with the results of a standard predictive control MPC applied to control a nonlinear system with parameter uncertainties and time-delays.

A note on the positive boundary robust stability of linear control systems

A note on the positive boundary robust stability of linear control systems

Mixed Incremental H ∞ and Incremental Passivity Analysis for Markov Switched Stochastic Nonlinear Systems

The current study addresses the mixed incremental H∞ and incremental passivity analysis for Markov switched stochastic (MSS) nonlinear systems. The multiple Lyapunov functions approach and the structure of Markov framework are utilized to establish some sufficient conditions for the MSS nonlinear systems, which will be used for the incrementally globally asymptotically stable in the mean(IGASiM) and performance index analysis. Then, the mixed incremental H∞ and incremental passivity performance issues are solved for two instances: in the first case, all subsystems are not IGASiM, while in the second one, both of IGASiM and unstable subsystems exist. Hence, it is shown that when none of the subsystems is IGASiM, the MSS nonlinear systems are IGASiM and possess the mixed incremental H∞ and incremental passivity performance metric in the presence of specified conditions. The mathematical induction is selected to guarantee the robust incremental stability of MSS systems with IGASiM and non-IGASiM subsystems and the performance index can be exhibited a prescribed decay rate. The effectiveness of the proposed results is demonstrated by two simulation examples.

Decentralized PID Controller Tuning Based on Nonlinear Optimization to Minimize the Disturbance Effects in Coupled Loops

Decentralized proportional-integral-derivative (PID) control systems are widely used for multiple-input multiple-output (MIMO) control problems. However, decentralized controllers cannot suppress the plant interactions in multivariable systems, which are addressed in the controller tuning phase. In this paper, a decentralized PID tuning method is proposed in order to minimize the undesirable effects of the coupling between the inputs and outputs of the closed-loop system. For this purpose, the PID parameter tuning method solves a nonlinear optimization problem. This optimization problem is formulated with the criteria of the performance, robustness and multivariable stability of the closed-loop system. A single design parameter is required to specify the trade-off between performance and robustness. Simulation studies are conducted to demonstrate the effectiveness of the proposed method. The performance is compared to that of alternative tuning techniques from the literature. Results show that the proposed approach is a feasible candidate for industrial application, as it is simple to implement and capable of addressing robustness and stability concerns of plant operators.

Broadband cavity enhanced absorption spectroscopy for measuring atmospheric NO&lt;sub&gt;3&lt;/sub&gt; radical

NO&lt;sub&gt;3&lt;/sub&gt; radical is the most important oxidant in atmospheric chemistry at night, and it controls the oxidation and removal of various trace gas components in the atmosphere. The understanding of the chemical process of NO&lt;sub&gt;3&lt;/sub&gt; radical is of great significance for studying the atmospheric pollution processes such as haze. The NO&lt;sub&gt;3&lt;/sub&gt; radical has a low concentration and strong activity, so it is relatively difficult to measure accurately. We report here in this paper an instrument for unambiguously measuring NO&lt;sub&gt;3&lt;/sub&gt; based on broadband cavity enhanced absorption spectroscopy (BBCEAS). To achieve the robust performance and system stability under diverse conditions, this BBCEAS instrument has been developed, with efficient sampling, and resistance against vibration and temperature change improved, and the BBCEAS instrument also has low-power consumption. The 660-nm-wavelemngth light-emitting diode (LED) is used as a light source of the BBCEAS system. The sampling gas path with low loss and suitable for domestic high-particle environment is designed. Through the LED light source test, the optimal working current and temperature can be obtained to achieve the acquisition of NO&lt;sub&gt;3&lt;/sub&gt; absorption spectrum with high signal-to-noise ratio. Considering the fact that the water vapor absorption is an important interference factor for the measurement of NO&lt;sub&gt;3&lt;/sub&gt; radical by BBCEAS, the daytime atmospheric measurement spectrum is used as a background spectrum, and participates in spectral fitting of NO&lt;sub&gt;3&lt;/sub&gt; to reduce the effect of water vapor. The mirror reflectivity and effective cavity length are calibrated, and the Allan variance analysis is also carried out. The reflectance of the mirror can reach about 0.99993 at 662 nm (NO&lt;sub&gt;3&lt;/sub&gt; absorption peak), and the corresponding theoretical effective optical path can reach more than 7 km, which can meet the measurement requirements of atmospheric NO&lt;sub&gt;3&lt;/sub&gt; radicals. The detection limit (1σ) of 0.75 pptv for NO&lt;sub&gt;3&lt;/sub&gt; is achieved with an acquisition time of 10 s and a total measurement error of about 16%. The atmospheric NO&lt;sub&gt;3&lt;/sub&gt; radical observation is carried out in Hefei. During the observation period, the highest NO&lt;sub&gt;3&lt;/sub&gt; concentration is 23.4 pptv, demonstrating the promising potential applications in in-situ, sensitive, accurate and fast simultaneous measurements of NO&lt;sub&gt;3&lt;/sub&gt; in the future by using the developed broadband cavity enhanced absorption spectroscopy.

Multi-Objective Optimal Control for Uncertain Singularly Perturbed Systems

This paper studies the passive multi-objective optimal control of uncertain singularly perturbed systems. First, the uncertainty is described in a norm-bounded way, and then the state space model of the system is determined. Further time, the problem of passivity can also be transformed into a linear quadratic performance index problem. According to the Lyapunov stability theory, the system robust stability criterion is derived, based on the above conclusion, the corresponding parameterized passive multi-objective controller is designed using state feedback, and the weight matrix and the minimum performance index are solved based on the optimal control theory. Finally, a numerical example is given to illustrate the correctness and feasibility of the control method.

Operator-based robust stability for nonlinear systems with multiple uncertainties using coprime factorisation method

In this paper, the robust stability of nonlinear systems with multiple uncertainties is considered by using a composite operator-based coprime factorisation method. Firstly, as for the exogenous external disturbance, the disturbance model is considered and the disturbance output is guaranteed to be bounded. Meantime, the adverse effect resulting from it is transformed to an equivalent effect on the stable part of the systems. By using operator-based coprime factorisation method, a feasible framework on multiple uncertainties is obtained. Then, the obtained equivalent effects resulting from the modelled disturbance and adverse effect from the internal perturbation are unified and addressed. Thirdly, sufficient conditions on guaranteeing robust stability of the considered nonlinear systems are considered by using robust coprime factorisation method, for relaxing computation burden on Bezout identity and avoiding requirement on knowing the perturbation signal. Based on the proposed conditions, two controllers are designed and the robust stability of the considered systems is proved. Finally, simulation results are shown to explain the proposed design scheme and confirm its effectiveness of this paper.

A polytopic strategy for improved non-asymptotic robust control via implicit Lyapunov functions

This paper is concerned with finite- and fixed-time robust stabilization of uncertain multi-input nonlinear systems via the implicit Lyapunov function method. Instead of splitting the system into a linear nominal model and an additive perturbation which gathers nonlinearities, parametric uncertainties, and exogenous disturbances, the methodology hereby proposed preserves some nonlinear terms in the nominal system via an exact polytopic representation which leads to design conditions in the form of linear matrix inequalities. As a result, feasible solutions are found where former approaches fail; these solutions have more accurate settling-time estimates with reduced control effort. The corresponding control law includes well-known high-order sliding modes as a particular case. Numerical simulations are provided to illustrate the advantages of the proposal.