Robust Stability Of System Research Articles

Robust Stability and Stable Member Problems for Multilinear Systems

In this paper, we consider robust stability and stable member problems for linear systems whose characteristic polynomials are nonmonic polynomials with multilinear uncertainty. For both problems, the results are given by using the reflection (box) coefficients and the extreme point property of multilinear functions defined on the box. Finding stable member in a polynomial family is one of the hard problems of linear control theory. This issue is considered by visualizing the cases n-l=2 and n-l=3. Necessary and sufficient conditions for robust stability and the existence of a stable member of the multilinear polynomial family using the reflection coefficients are obtained. Several examples are provided.

A Generalization of Routh–Hurwitz Stability Criterion for Fractional-Order Systems with Order α ∈ (1, 2)

Based on the generalized Routh–Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order α∈1,2, called the fractional-order Routh–Hurwitz criterion. Compared with the existing criterion, ours involves fewer and simpler expressions, which is significant for analyzing the robust stability of high-dimensional uncertain systems. All these expressions are explicit ones about the coefficients of the characteristic polynomial of the system matrix, so the stable parameter region of fractional-order systems can be described directly. Some examples show the effectiveness of our method.

Lyapunov characterizations on input-to-state stability of nonlinear systems with infinite delays

This paper addresses Lyapunov characterizations on input-to-state stability (ISS) of time-varying nonlinear systems with infinite delays. With novel ISS definitions in the case of nonlinear systems with infinite delays, we present several results on their ISS Lyapunov characterizations in the form of both ISS Lyapunov theorems and converse ISS Lyapunov theorems. It is shown that an infinite-delayed system is (locally) ISS if it has a (local) ISS Lyapunov functional, and conversely, there exists a (local) ISS Lyapunov functional if it is (locally) ISS. To prove the converse ISS Lyapunov theorems, we establish a key technical lemma bridging ISS/LISS and robust asymptotic stability of systems with infinite delays and two converse Lyapunov theorems concerning robust asymptotic stability of systems with infinite delays. Two distinctive advantages of this work are that a large class of infinite dimensional spaces are allowed and the results are established based on a more general Lipschitz condition, i.e., the right hand side Lipschitz (RS-L) condition. An example is provided for illustration of the obtained results.

Non-fragile Robust Stabilization of Nonlinear Uncertain Switched Systems with Actuator Saturation

Non-fragile Robust Stabilization of Nonlinear Uncertain Switched Systems with Actuator Saturation

Linkage-constraint criteria for robust exponential stability of nonlinear BAM system with derivative contraction coefficients and piecewise constant arguments

This paper presents linkage-constraint criteria to guarantee the robustness of global exponential stability (RoGES) for a class of generalized nonlinear bidirectional associative memory (BAM) systems in the presence of derivative contraction coefficients and piecewise constant arguments (NBAM-dp system). However, because of the appearance of the tricky derivative compression coefficients and coupling relation with piecewise constant arguments, the previous Gronwall inequality is not applicable here. Thus, by means of generalized Gronwall inequality and norm inequality techniques, an independent parameters and interdependent variables (IPIV) principle is designed to solve the implicit bivariate transcendental equations to provide the respective supremum of the two interference factors, and the major criteria for guaranteeing the RoGES for NBAM-dp systems are obtained accordingly. Meanwhile, according to the IPIV principle, the relationship between the above two interference factors reflected in the linkage-constraint criteria is ensured to be mutually constrained and dynamically interconnected. Finally, comparative simulations and auxiliary data are provided to demonstrate the effectiveness of the theoretical findings.

Dynamic output feedback robust [formula omitted] control of networked control systems with time-Varying delays via T-S fuzzy models

This paper addresses the problem of robust stabilization for networked control systems (NCS) where the stochastic behavior of the network does not allow correct and complete transmission of data to both the actuators and the controller. The objective is to model the NCS using Takagi-Sugeno (T-S) fuzzy systems with uncertainties and external disturbances and to design a time-varying delay fuzzy controller such that the closed-loop system is robustly exponentially stable with a prescribed decay rate. Sufficient conditions are derived using the delay-dependent Lyapunov-Krasovskii functional with a robust H∞ controller in terms of linear matrix inequalities (LMIs). Accordingly, desired fuzzy controllers are designed by using feasible solutions to the obtained LMIs. The proposed fuzzy controller can keep the T-S fuzzy system stable in the presence of time-varying delay, uncertainties, and external disturbance. Two numerical examples with different conditions on parameters are provided to illustrate the performance and robustness of the proposed approach.

Active disturbance rejection control for non-minimum phase systems under plant reconstruction

Active disturbance rejection control (ADRC) for non-minimum phase (NMP) systems is a challenging problem due to the conflict between stability and feedback tuning. The key point on this issue is to avoid heavy feedback tuning for robustness enhancement. We perform plant reconstruction to obtain an explicit expression of internal disturbance, such that it can be reduced by cascade compensation. Then, a new ADRC scheme is developed based on plant reconstruction and the internal stability criterion for ADRC system is derived. The stability conditions provide guidelines on the design of the cascade compensator and disturbance observer. It also indicates that the cascade compensation contributes to the robust stability of NMP systems. Simulation results of two typical NMP systems are provided to show the efficacy of the proposed ADRC scheme. Physical realizability is also demonstrated through experiments on a motion NMP system.

Networked robust stability for linear time-varying systems

A networked control system (NCS) with the communication channels described by cascaded two-port networks for linear time-varying systems is studied. In this framework, a system is considered as a (possibly unbounded) linear operator that maps an input space to an output space. We consider the operator norm bounded uncertainties in the transmission matrices of two-port networks as well as the gap-type uncertainties in the plant and controller. A necessary and sufficient condition for robust stability of the NCS is generalized from the time-invariant case.

Substrate-inducible and antibiotic-free high-level 4-hydroxyvaleric acid production in engineered Escherichia coli

In this study, we developed a levulinic acid (LA)-inducible and antibiotic-free plasmid system mediated by HpdR/P hpdH and infA-complementation to produce 4-hydroxyvaleric acid (4-HV) from LA in an engineered Escherichia coli strain. The system was efficiently induced by the addition of the LA substrate and resulted in tight dose-dependent control and fine-tuning of gene expression. By engineering the 5′ untranslated region (UTR) of hpdR mRNA, the gene expression of green fluorescent protein (GFP) increased by at least two-fold under the hpdH promoter. Furthermore, by evaluating the robustness and plasmid stability of the proposed system, the engineered strain, IRV750f, expressing the engineered 3-hydroxybutyrate dehydrogenase (3HBDH∗) and formate dehydrogenase (CbFDH), produced 82 g/L of 4-HV from LA, with a productivity of 3.4 g/L/h and molar conversion of 92% in the fed-batch cultivation (5 L fermenter) without the addition of antibiotics or external inducers. Overall, the reported system was highly beneficial for the large-scale and cost-effective microbial production of value-added products and bulk chemicals from the renewable substrate, LA.

Quadcopter UAVs Extended States/Disturbance Observer-Based Nonlinear Robust Backstepping Control.

A trajectory tracking control for quadcopter unmanned aerial vehicle (UAV) based on a nonlinear robust backstepping algorithm and extended state/disturbance observer (ESDO) is presented in this paper. To obtain robust attitude stabilization and superior performance of three-dimension position tracking control, the construction of the proposed algorithm can be separated into three parts. First, a mathematical model of UAV negatively influenced by exogenous disturbances is established. Following, an extended state/disturbance observer using a general second-order model is designed to approximate undesirable influences of perturbations on the UAVs dynamics. Finally, a nonlinear robust controller is constructed by an integration of the nominal backstepping technique with ESDO to enhance the performance of attitude and position control mode. Robust stability of the closed-loop disturbed system is obtained and guaranteed through the Lyapunov theorem without precise knowledge of the upper bound condition of perturbations. Lastly, a numerical simulation is carried out and compared with other previous controllers to demonstrate the great advantage and effectiveness of the proposed control method.

Definition of General Operator Space and The s-gap Metric for Measuring Robust Stability of Control Systems with Nonlinear Dynamics

Definition of General Operator Space and The s-gap Metric for Measuring Robust Stability of Control Systems with Nonlinear Dynamics

Delay-dependent criteria for robust stability and stabilization of fractional-order time-varying delay systems

In this paper, the robust stability and stabilization problems for fractional-order time-varying delay systems are investigated. Firstly, a new fractional-order Razumikhin theorem is given. By using the proposed fractional-order Razumikhin theorem, novel delay-dependent stability conditions for both nominal and uncertain linear fractional-order time-varying delay systems are derived. The results are in form of linear matrix inequalities, which are convenient for application and calculation. Then, the obtained stability conditions are utilized to derive a state feedback stabilization controller. To tackle the computational difficulty of the controller design method, a local optimization algorithm is proposed. Finally, three examples are provided to illustrate that the proposed results are valid and less conservative.

Disturbance rejections of interval type-2 fuzzy systems under event-triggered control scheme

The problem of robust stabilization of interval type-2 fuzzy systems are studied by using equivalent-input-disturbance estimator-based event-triggered fuzzy control scheme. The estimator of the addressed system is designed by introducing new membership functions and then by using the same premises of the observer, the fuzzy controller is designed. To be precise, sampling-based event-triggered scheme is taken into the account in the controller design to save the communication resources and avoid the existence of Zeno behaviour. Furthermore, to compensate the impact of unknown disturbance, the equivalent-input-disturbance estimator-block is included as an internal loop of closed-loop system. To derive the stability conditions, a novel type of sampling-dependent piece-wise Lyapunov-Krasovskii functional is constructed. Then, by introducing slack matrices, the fuzzy membership function dependent stability criteria are derived. The event-triggered weighting matrix and the gains of controller and observer can be obtained by obtaining the solutions of the developed stability criteria. At last, numerical simulations are given to reflect the effectiveness and applicability of the developed theoretical results.

Robust Finite-Time Stability for Uncertain Discrete-Time Stochastic Nonlinear Systems with Time-Varying Delay.

The main concern of this paper is finite-time stability (FTS) for uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD) and multiplicative noise. First, a Lyapunov–Krasovskii function (LKF) is constructed, using the forward difference, and less conservative stability criteria are obtained. By solving a series of linear matrix inequalities (LMIs), some sufficient conditions for FTS of the stochastic system are found. Moreover, FTS is presented for a stochastic nominal system. Lastly, the validity and improvement of the proposed methods are shown with two simulation examples.

Delay-dependent and order-dependent stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay via linear matrix inequality approach

This paper concentrates on the robust stability and stabilization analysis of variable fractional order uncertain differential systems with time-varying delay. Firstly, by using a suitable Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems is proposed. Then, based on the above stability conditions, the robust delay-dependent and order-dependent stability conditions for the uncertain systems are discussed. Moreover, in order to stabilize the nominal and uncertain systems, state feedback controllers are also derived with the help of the presented stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.

Generalized PI control for robust stabilization of dynamical systems

This paper presents a generalization of existing control methods. The proposal stands for a novel control structure that enforces the robust stabilization of a large class of physical and engineering systems, which are subject to the effect of nonlinearities, disturbances and uncertainties. The proposed scheme results as a state feedback plus a generalized proportional–integral (PI) controller. The state feedback compensates vanishing uncertainties, while the generalized PI control term gets rid of the effect of matched uncertainties, where the assumption on the regularity of the disturbance is relaxed. The proposed contribution is the generalization of conventional PI structures to account for the case of more variate closed-loop responses. Although the usefulness of the studied generalization in real applications deserves further investigation, some numerical simulations show the pertinence of the proposed scheme.

Development and Validation of In-vitro dissolution test using RP-HPLC Analysis for simultaneous estimation of Azelnidipine and Telmisartan in a Fixed-dose Combination

The present analytical study aims to develop and validate the RP-HPLC method for dissolution of Azelnidipine (AZE) and Telmisartan (TEL) in fixed-dose combination tablets (8 mg/40 mg) and also to demonstrate that the test method used, is suitable for its intended purpose as per ICH guidelines. The protocol developed utilizes Inertsil ODS 3V, C18 column 150 x 4.6 mm, 5 µm particle sizes, column oven temperature 40°C with a flow rate of 1.5 mL/min. The volume of injection was kept at 10 µL and run time 11.0 minutes at 254 nm using Acetonitrile and buffer as mobile phase in gradient mode. Thus developed method after validating on different parameters was found to be complying with system suitability, specificity, precision, intermediate precision, accuracy, linearity, robustness, and solution stability found to meet the predetermined acceptance criteria.

On the robust stability of commensurate fractional-order systems

Based on a recent generalised version of the Mikhailov stability criterion, this paper presents a Kharitonov–like test for a class of linear fractional–order systems described by transfer functions whose coefficients are subject to interval uncertainties. To this purpose, first the transfer function is associated with an integer-order complex polynomial function of the generalised frequency (i.e. the current coordinate along the boundary radii of the instability sector) whose coefficients are uncertain. Then the geometrical form of the value set of this characteristic polynomial is determined from the direct examination of its monomial terms. To show how the test operates, it is finally applied to two fractional–order transfer functions whose coefficients belong to given intervals.

Gradient RP-HPLC method development and validation for simultaneous estimation of paclitaxel and albendazole

The goal of this research is to provide an accurate and exact technique for estimating Albendazole and Paclitaxel simultaneously utilizing gradient RP-HPLC (high performance liquid chromatography). A UV detector fixed at 230 nm was used to estimate albendazole and paclitaxel simultaneously. As the solvent system, acetonitrile and water in the ratio of 50:50 was used in the presence of 0.1 % trifluoroacetic acid. Mobile phase was run on a Inertsil ODS 3V 150 4.6 mm or equivalent column in Gradient mode at a flow rate of 1.0 mL/min. By this method albendazole and paclitaxel showed 6.199 and 9.684 retention time (Rt) respectively with continuous run upto 25 min. In the prescribed concentration range, the calibration curves for each analyte were determined to be linear (r2 > 0.994). The percentage of recovery was found to be within the limit at each level (98.0 %to 102.0 %). All validation parameters were determined to be acceptable, including system precision, method precision, linearity, range, accuracy, ruggedness, robustness, solution, and mobile phase stability findings. This suggests that the HPLC simultaneous approach for determining albendazole and paclitaxel assays is accurate. S

Parameter-dependent Lyapunov function based fault estimation and fault-tolerant control for LPV systems

In this paper, an integrated fault estimation (FE) and fault-tolerant control (FTC) method is proposed for linear parameter varying (LPV) systems using the parameter-dependent Lyapunov function. The observer-based estimation and fault-tolerant control structure causes an uncertainty between systems which is called the bi-directional uncertainty. Additionally, with simultaneous actuator and sensor faults, disturbances, the overall performance of the FTC system decreases. To maintain robust stability of closed-loop systems, an unknown input observer fault estimator approach with both state feedback control and sliding mode control is implemented as a solution by solving optimisation using a linear matrix inequality (LMI) formulation. The efficiency of the integrated FE/FTC design is demonstrated using the pitch-axis missile LPV model and simulated to evaluate the merits of the suggested approach.