Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Rules for confidence intervals of permeability coefficients for water flow in over-broken rock mass

Based on the steady-state seepage method, we used the Mechanical Testing and Simulation 815.02 System and a self-designed seepage instrument for over-broken stone to measure seepage properties of water flows in three types of crushed rock samples. Three methods of confidence interval in describing permeability coefficients are presented: the secure interval, the calculated interval and the systemic interval. The lower bound of the secure interval can be applied to water-inrush and the upper bound can solve the problem of connectivity. For the calculated interval, as the axial pressure increases, the length of confidence interval is shortened and the upper and lower bounds are reduced. For the systemic interval, the length of its confidence interval, as well as the upper and lower bounds, clearly vary under low axial pressure but are fairly similar under high axial pressure. These three methods provide useful information and references for analyzing the permeability coefficient of over-broken rock.

Graphic theory on interval stability of networked control systems

A new method on the interval stability of networked control systems （NCSs） with random delay and data packet dropout is studied. Combining interval systems and NCSs, a graphic condition on judging interval stability is presented in terms of the weighted diagraph theory in graph theory. Furthermore, utilizing the graph-theoretic algorithm, the delay-depended controller gains are obtained. Aiming at the same delay and data packed dropout, several controller gains are obtained, simultaneously. The example and simulation illustrate the effectiveness of the proposed method.

A Note on Robust Stability Analysis of Fractional Order Interval Systems by Minimum Argument Vertex and Edge Polynomials

By using power mapping(s =v^m),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.

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters

The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov- Krasovskii functional and employing the decomposition technique of interval matrix and Ito＇s formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.

Leader-following consensus control for networked multi-teleoperator systems with interval time-varying communication delays

We study the leader-following consensus stability and stabilization of networked multi-teleoperator systems with interval time-varying communication delays. With the construction of a suitable Lyapunov–Krasovskii functional and the utilization of the reciprocally convex approach, novel delay-dependent consensus stability and stabilization conditions for the systems are established in terms of linear matrix inequalities, which can easily be solved by various effective optimization algorithms. One illustrative example is given to illustrate the effectiveness of the proposed methods.

Attribute Reduction in Interval and Set-Valued Decision Information Systems

In many practical situation, some of the attribute values for an object may be interval and set-valued. This paper introduces the interval and set-valued information systems and decision systems. According to the semantic relation of attribute values, interval and set-valued information systems can be classified into two categories: disjunctive (Type 1) and conjunctive (Type 2) systems. In this paper, we mainly focus on semantic interpretation of Type 1. Then, we define a new fuzzy preference relation and construct a fuzzy rough set model for interval and set-valued information systems. Moreover, based on the new fuzzy preference relation, the concepts of the significance measure of condition attributes and the relative significance measure of condition attributes are given in interval and set-valued decision information systems by the introduction of fuzzy positive region and the dependency degree. And on this basis, a heuristic algorithm for calculating fuzzy positive region reduction in interval and set-valued decision information systems is given. Finally, we give an illustrative example to substantiate the theoretical arguments. The results will help us to gain much more insights into the meaning of fuzzy rough set theory. Furthermore, it has provided a new perspective to study the attribute reduction problem in decision systems.

LMI conditions for quadratic and robust D-stability of interval systems

Sufficient conditions for the quadratic D-stability and further robust D-stability of interval systems are presented in this paper. This robust D-stability condition is based on a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities （LMIs） defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as in previous results. The results contain the usual quadratic and robust stability of continuous-time and discrete-time interval systems as particular cases. The illustrative example shows that this method is effective and less conservative for checking the quadratic and robust D-stability of interval systems.

Stability analysis of T-S fuzzy control systems with interval plants

The stability of a type of Takagi-Sugeno ( T-S) fuzzy control systems is considered. The plant of T-S fuzzy system has parameter uncertainties. By using the off-axis circle criterion and Kharitonov Theorem,a sufficient condition is derived to analyze the global asymptotic stability of T-S fuzzy control system. The proposed method has a graphical explanation which facilitates stability analysis. A numerical example is also given to demonstrate how to use our approach in analyzing certain T-S fuzzy control systems.

Stabilization and H-infinity control for interval descriptor systems

This paper considers H-infinity control problem for interval descriptor systems. Necessary and sufficient LMI-based conditions are derived for quadratic-like H-infinity control analysis of interval descriptor systems. Using the analysis result, two types of feedback controllers are designed so that the closed-loop interval descriptor systems are admissible with H-infinity-norm less than a prescribed value. To the best of the authors＇s knowledge, this is the first paper to deal with the H-infinity control problem of interval descriptor systems in the literature.

Robust Stability Criteria for Neutral Systems with Interval Time-Varying Delays and Nonlinear Perturbations

This paper investigates the problem of delay-dependent robust stability analysis for a class of neutral systems with interval time-varying delays and nonlinear perturbations. Such nonlinear perturbations are with time-varying but norm-bounded characteristics. Based on a new Lyapunov-Krasovskii functional, together ,sith a free-weighting matrices technique, improved delay-dependent stability criteria are established. It is shown that less conservative results can be obtained in terms of linear matrix inequalities （LMIs）. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed approach.

Robust stability test for 2-D continuous-discrete systems with interval parameters

It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.

An Interval Programming-based Traffic Planning Model for Urban Vehicle Emissions Management

An interval linear traffic planning model is developed for supporting vehicle emissions limited under uncertainty. The interval linear traffic planning model can address uncertainties of traffic system and vehicle emissions related to system costs and limitation of emission. The interval linear traffic planning model is applicable to complex traffic system. One virtual city as our study object was taken by using the interval linear traffic planning model. In this study, one virtual case and a scenario are provided for three planning periods. The results indicate that the interval linear traffic planning model can effectively reduce the vehicles emission and provide strategies for authorities to deal with problems of transportation system.

Componentwise Asymptotic Stability of Continuous-Time Interval Systems

A special type of asymptotic (exponential) stability, namely componentwise asymptotic (exponential) stability for the continuous-time interval system is investigated. A set-valued map that represents the constraint of the state of the system is defined. And, by applying the viability theory of differential equation, sufficient and necessary conditions for the componentwise asymptotical (exponential) stability of this kind of systems are given.

Distribution of non-Markovian intervals for open qubit systems

We study the non-Markovianity of open qubit systems using the measure N proposed by Breuer, Laine and Piilo [Phys. Rev. Lett. 103 210401 （2009）]. We find that for the three types of quantum noises, amplitude-damping, dephasing and depolarizing noises, there exist some non-Markovian time intervals whose distribution is independent of the selection of the pair of initial states. Therefore, the maximization in the definition of measure N can be actually removed without influencing the detection of non-Markovianity.

Sufficient Conditions for Robust Stability of Discrete Large-Scale Interval Systems with Multiple Time Delays

The robust stability analysis for discrete large-scale uncertain systems with multiple time delays is addressed in this paper. We establish a method for selecting properly a positive definite matrix Q to derive a very simple upper solution bound of the discrete algebraic Lyapunov equation (DALE). Then, using the Lyapunov equation approach method with this upper bound, several sufficient conditions are presented to guarantee the robust stability of the overall systems. Comparisons between the proposed results with a previous one are also given.

Stable Routh-Padé-type approximation in model reduction of interval systems

An interval Pade-type approximation is introduced and then Routh-Pade-type method （IRPTM） is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical

An On-Line Modeling Based Kalman Filtering Process for Time-Interval-Variable Sequences with Application to Astronomic Surveying

The problem of variable sampling time interval which appears in application of Kalman Filtering is analyzed and the corresponding filtering process with or without present transition matrix is suggested, then an application experiment for astronomical surveying is introduced. In this process, the known stochastically variable sampling time intervals play the roles as deterministic input sequences of the state-space description, and the corresponding matrix and (if needed) state transition matrix can be established by performing real-time and structure-linear system identification.