Stability Criteria For Systems Research Articles

Curved road traffic flow car-following model and stability analysis

To find the characteristics of curved road traffic flow, we propose a new car-following model based on the typical full velocity difference model, and analyze the model stability condition with system state space method and control system stability criteria. With numerical simulation, the stability and feasibility of the model are proved. Under the condition of same initialization traffic flow density, with the increase of road curve, traffic flow stability decreases. Our study is greatly helpful for traffic control and management at road curve site.

Stability criteria of a class of nonlinear impulsive switching systems with time-varying delays

This paper investigates stability problems of a class of nonlinear impulsive switching systems with time-varying delays. Based on the common Lyapunov function method and Razumikhin technique, several stability criteria are established for nonlinear impulsive switching systems with time-varying delays. Our results show that switching systems can be stabilized by impulsive switching signals even if the system matrices are all unstable. In the absence of impulses, some of our results reduce to similar stability criteria for nonimpulsive switching systems in some recent research articles. Several examples with simulations are given to illustrate the efficiency of our results.

Performance Analysis of Modified Smith Predictor for Integrating and Time-Delay Processes

A modified Smith predictor design for higher-order processes with an integrator and longer dead-time is proposed in this paper. The controller used in this Smith predictor is an Integral-Proportional Derivative controller. The main objective of this work was to design a dead-time compensator (DTC) to obtain a critically damped system that was as fast as possible in its set point and load disturbance rejection performance. The controller described in this paper is tuned using an adaptive method. The system's stability criteria were analysed for a two-degree-of-freedom self-adaptive controller with respect to phase margin and time constant, and compared with the modified smith predictor concept using adaptive tuning techniques. The Smith predictor's robustness was verified for integrating and time delay processes and also with first-order systems with time delay processes.

Stability criteria for linear Hamiltonian dynamic systems on time scales

Abstract In this article, we establish some stability criteria for the polar linear Hamiltonian dynamic system on time scales x Δ ( t ) = α ( t ) x ( σ ( t ) ) + β ( t ) y ( t ) , y Δ ( t ) = - γ ( t ) x ( σ ( t ) ) - α ( t ) y ( t ) , t ∈ T by using Floquet theory and Lyapunov-type inequalities. 2000 Mathematics Subject Classification: 39A10.

Improved delay-dependent stability criteria for systems with interval delay

Improved delay-dependent stability criteria for systems with interval delay

Can we prove stability by using a positive definite function with non sign-definite derivative?

Novel criteria for global asymptotic stability of nonlinear uncertain finite-dimensional systems are presented. The results are obtained by a combination of the discretization approach and the ideas contained in the proof of the original Matrosov's result. The results can be used for the proof of global asymptotic stability by using continuously differentiable, positive definite functions which do not have a negative semi-definite derivative. Illustrating examples are provided.

Stability criterion with less LMI variables for linear discrete-time systems with additive time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality (LMI) variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

Impedance-Based Stability Criterion for Grid-Connected Inverters

Grid-connected inverters are known to become unstable when the grid impedance is high. Existing approaches to analyzing such instability are based on inverter control models that account for the grid impedance and the coupling with other grid-connected inverters. A new method to determine inverter-grid system stability using only the inverter output impedance and the grid impedance is developed in this paper. It will be shown that a grid-connected inverter will remain stable if the ratio between the grid impedance and the inverter output impedance satisfies the Nyquist stability criterion. This new impedance-based stability criterion is a generalization to the existing stability criterion for voltage-source systems, and can be applied to all current-source systems. A single-phase solar inverter is studied to demonstrate the application of the proposed method.

Asymptotic stability criterion for nonlinear monotonic systems and its applications (review)

This paper discusses uniform asymptotic stability criteria for nonlinear monotonic systems and their applications in various problems of nonlinear dynamics and population dynamics

Robust stability criteria for uncertain linear systems with interval time-varying delay

This paper considers the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay and proposes less conservative stability criteria for computing the maximum allowable bound of the delay range. Less conservatism of the proposed stability criteria is attributed to the delay-central point method of stability analysis, wherein the delay interval is partitioned into two subintervals of equal length, and the time derivative of a candidate Lyapunov-Krasovskii functional based on delay decomposition technique is evaluated in each of these delay segments. In deriving the stability conditions in LMI framework, neither model transformations nor bounding techniques using free-weighting matrix variables are employed for dealing the cross-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional; instead, they are dealt using tighter integral inequalities. The proposed analysis subsequently yields a stability condition in convex LMI framework that can be solved using standard numerical packages. For deriving robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties, are considered. The effectiveness of the proposed stability criteria is validated through standard numerical examples.

Influence of internal heat removal upon effectiveness, stability of an exothermic catalytic film: Implications for process intensification

Microreactors employing thin catalytic films present a unique situation in catalyst design owing to the removal of symmetric internal boundary condition (i.e. zero heat flux) employed in catalyst design analysis to-date. The allowance for substantial heat removal and/or addition rates at the internal boundary of the catalytic film via process intensification (e.g. heat-exchanger reactors, recuperative combustors) can have significant implications on catalyst effectiveness and ignition/extinction behavior. This manuscript presents a simplified one-dimensional model of two catalytic thin films exchanging heat through a common dividing wall to demonstrate the importance of catalyst design for the cases of (i) internal cooling or heating of a catalytic film, and (ii) coupling of exothermic and endothermic reactions via separate catalytic films. The former case is analogous to microreactor designs for heat removal from an exothermic process, while the latter addresses catalyst design for heat-exchanger reactors coupling endothermic reactions (e.g. steam reforming) with exothermic reaction (e.g. partial oxidation). For a single film catalyzing an exothermic reaction, internal cooling was found to expand the region of steady-state multiplicity and simultaneously decrease catalyst effectiveness, whereas internal heating resulted in stabilization. For the case of two films separately catalyzing exothermic and endothermic reactions and exchanging heat via a common supporting wall, a combination of high wall thermal conductance and intermediate Thiele modulus for the endothermic reaction was capable of preventing ignition/extinction behavior while maintaining individual film effectivenesses in excess of unity. These findings not only give practical insight into the intrinsic behavior of catalysts employed in recuperative and heat-exchanger reactors, but also illustrate the need for future development of rigorous stability criteria for such systems.

Two effective stability criteria for linear time-delay systems with complex coefficients

This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex-DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization (ETDAS) control and n time delay auto-synchronization (NTDAS) control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.

A passivity-based stability criterion for reaction diffusion systems with interconnected structure

In this paper, stability of a class of reaction diffusion systems is studied. Conditions on global asymptotic stability of the homogeneous equilibrium are derived based on the diagonal stability of a dissipativity matrix. This work extends previous result on global asymptotic stability from cyclic systems to general systems with interconnected structure. In addition, it reformulates the approach using an input-output formalism that makes the results easier to understand and apply. A biological example from the Mitogen-Activated Protein Kinase (MAPK) system is provided at the end to illustrate the new approach and the main result.

Improved delay-dependent robust stability criteria for uncertain time delay systems

This paper deals with the robust stability analysis for uncertain systems with time-varying delay. New delay-dependent robust stability criteria of uncertain time-delay systems are proposed by exploiting appropriate Lyapunov functional candidate. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism, due to the introduction of a method to estimate the upper bound of the derivative of Lyapunov functional candidate without ignoring the additional useful terms. Numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method.

New Stability Criteria for Linear Systems with Interval Time-varying State Delays

In the present paper, the problem of stability analysis for linear systems with interval time-varying delays is considered. By introducing a new Lyapunov-Krasovskii functional, new stability criteria are derived in terms of linear matrix inequalities (LMIs). Two numerical examples are given to show the superiority of the proposed method.

On Nonsingularity Verification of Uncertain Matrices Over a Quadratically Constrained Set

Nonsingularity of a matrix is investigated in this technical note that depends affinely on several uncertainty matrices whose real and imaginary parts are constrained by some quadratic forms. Based on some equivalent descriptions for these uncertainty matrices, a sufficient condition is derived. This condition is given in a linear matrix inequality form and can in principle be efficiently validated. The obtained result includes some well known results in systems and control theory as a special case, such as the Lyapunov equation based stability criterion for linear time invariant systems, the (D,G)-scaling based upper bound for the mixed structured singular value, a sufficient condition for the stability of spatially interconnected systems, etc. A computationally verifiable condition is also provided that indicates situations under which the aforementioned condition becomes necessary.

On disconjugacy and stability criteria for discrete Hamiltonian systems

By making use of new Lyapunov type inequalities, we establish disconjugacy and stability criteria for discrete Hamiltonian systems. The stability criteria are given when the system is periodic.

Asymptotic stability and instability criteria for nonautonomous systems

The classical criterion of asymptotic stability of the zero solution of equations x′ = f(t, x) is that there exists a function V (t, x), a(∥x∥) ≤ V (t, x) ≤ b(∥x∥) for some a, b ∈ K such that $$ \dot{V} $$ (t, x) ≤ −c(∥x∥) for some c ∈ K. In this paper, we prove that if $$ \mathop {V}\limits^{(m + {1})} $$ (t, x) is bounded on some set [tk − T, tk + T] × BH(tk → +∞ as k → ∞), then the condition that $$ \dot{V} $$ (t, x) ≤ −c(∥x∥) can be weakened and replaced by that $$ \dot{V} $$ (t, x) ≤ 0 and − (− $$ \dot{V} $$ (tk, x)| + − $$ \ddot{V} $$ (tk, x)| + ⋯ + − $$ \mathop {V}\limits^{(m)} $$ (tk, x)|) ≤ −c′(∥x∥) for some c′ ∈ K. Moreover, the author also presents a corresponding instability criterion. [1–10]

Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative

This paper discretizes the states, a method introduced in [18] for constant delayed systems, not only in constructing the Lyapunov–Krasovskii (L–K) functional but also in designing the integral inequality technique [17,19] for time-varying delayed systems, which increase the order of uncorrelated augmentation [5,21,22]. Based on the discretized state, [10,27]'s piecewise analysis method is applied to confirm the system stability in whole delay bound. Asymmetric variation of the delay derivative is assumed so that direct extension to all constraints of the delay derivative can be achieved. Examples show the resulting criteria improve the allowable delay bounds over all existing ones in the literature.

Efficient calculation of operating security regions in power systems

Power system operators are often faced with the challenge of identifying the dynamic operating security modes during the on-line operation of the power system, which requires fast, accurate and reliable evaluation techniques. The system security constraints are in fact boundaries that surround all possible operating modes (scenarios) of the power system. In other words, these boundaries form the feasible operating domain - in the parameter space spanned by various operating variables - within which the system can safely be operated. For a given operating scenario, the associated security level is measured by the “distance” (for example, the Euclidean norm) of the operating point from the security region boundary. This paper presents a novel methodology and computerized scheme, which are capable of identifying dynamic operating security modes during the on-line operation of electric power systems. The methodology adopted in this paper includes the development of advanced, highly efficient computerized algorithms for fast identification of dynamic operating security modes of power systems. One of the salient outcomes of this paper is the development of a novel framework for identification and representation of operating security regions in power systems as well as evaluation of security levels associated with different operating scenarios. While the concepts and principles presented are general, the work of this paper is confined to the interpretation of the security boundary in terms of system stability criteria. In addition, the framework presented is applicable quite as well to other criteria that may be considered. Key words: Power system operation, security regions, system stability, operating constraints.