Stability Criteria For Systems Research Articles

A semi-empirical stability criterion for real planetary systems with eccentric orbits

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first-order mean motion resonance overlap. We show that this criterion fits the stability regions in real exoplanet systems quite well. In addition, we show that elliptical orbits can remain stable even for regions where the apocentre distance of the inner orbit is larger than the pericentre distance of the outer orbit, as long as the initial orbits are aligned. The analytical expressions provided here can be used to put rapid constraints on the stability zones of multiplanetary systems. As a byproduct of this research, we further show that the amplitude variations of the eccentricity can be used as a fast-computing stability indicator.

Passivity-based decentralized stabilization of multi-agent systems with uncertainty and mixed delays

In this paper, we investigate a decentralized stabilization problem of uncertain multi-agent systems with mixed delays including discrete and distributed time-varying delays based on passivity stability. We design a decentralized state-feedback stabilization scheme such that the family of closed-loop feedback subsystems enjoys the delay-dependent passivity stability for each subsystem. Then, by employing a new Lyapunov-Krasovskii function, a linear matrix inequality (LMI) approach is developed to establish the delay-dependent criteria for the passivity stability of multi-agent systems. The sufficient condition is given for checking the passivity stability. The proposed LMI result is computationally efficient. An example is given to show the effectiveness of the method.

Robust dynamic output feedback control of networked control systems with congestion control

This paper investigates a robust dynamic output feedback controller for networked control systems (NCSs) with a simple congestion control scheme. This scheme enables the NCSs design to enjoy advantages of both time-triggered and event-triggered systems. The proposed scheme compares current measurement with last transmitted measurement. If difference between them is less than a prescribed percentage of the current measurements then no measurement is transmitted to controller and the controller always uses the last transmitted measurements to calculate feedback gains. Moreover, this technique is applied to controller output as well. The stability criteria for closed-loop system is formulated using the Lyapunov-Krasovskii functional approach. The sufficient conditions for the controller are given in terms of solvability of bilinear matrix inequalities (BMIs). These BMIs are converted into quasi-convex linear matrix inequalities that are solved using the cone complementarity linearisation algorithm. A simulation example is used to evaluate how effective the simple congestion control scheme is in reducing network bandwidth.

On Improved Delay-Range-Dependent Stability Criteria for Linear Systems with Interval Time-Varying Delay

In this paper, we consider the problem of robust delay-dependent stability for a class of linear uncertain systems with interval time-varying delay. By using the directly Lyapunov-Krasovskii (L-K) functional method, integral inequality approach and the free weighting matrix technique, new less conservative stability criteria for the system is formulated in terms of linear matrix inequalities .Numerical examples are given to show the effectiveness of the proposed approach.

New criteria for exponential stability of nonlinear difference systems with time-varying delay

General nonlinear time-varying difference systems with time-varying delay are considered. Some new explicit criteria for global exponential stability are given. Two examples are given to illustrate the obtained results.

New results on stability analysis for neutral stochastic linear system

In this study, the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic linear system with mixed time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii functional and utilising a convex polyhedron method, some new delay-dependent exponential stability criteria for such system are established in forms of linear matrix inequalities, which have less conservatism. Finally, three illustrative numerical examples are given to show the effectiveness of the obtained results.

Exponential Stability Criteria for Neutral System with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.

Finite-Time Stability and Dynamic Output Feedback Stabilization of Stochastic Systems

This paper is concerned with finite-time stability and dynamic output feedback stabilization for Ito type stochastic systems. First of all, it presents a sufficient pth moment finite-time stability criterion of nonlinear stochastic systems. When linear stochastic systems are considered, a finite-time stability condition in the sense of mean square is obtained by choosing a quadratic Lyapunov function. Then, a dynamic output feedback controller is designed to mean-square finite-time stabilize the linear stochastic systems under consideration. Furthermore, the proposed method is extended to finite-time dynamic output feedback control for a class of linear stochastic retarded systems. Numerical examples are finally provided to show the effectiveness of the approach.

Stability analysis of complex-valued nonlinear delay differential systems

Since a quantum system, which is one of the foci of ongoing research, is a classical example of a complex-valued system, in this paper, the issue of asymptotic stability of solutions to complex-valued nonlinear delay differential systems is addressed. By taking advantage of the theory of matrix measure, the exponential stability criteria of a complex-valued nonlinear delay system are established, which not only improve some known results in literature, but also greatly reduce the complexity of analysis and computation. As an application, the exponential stability conditions of 2-dimensional real-valued time-varying delay systems are derived, the conditions are easier to verify in comparison with known results. The effectiveness of the main results are illustrated by some numerical examples.

Stability analysis of a novel epidemics model with vaccination and nonlinear infectious rate

In this paper, by considering pathogen evolution and human interventions behaviors with vaccines or drugs, we build up a novel SEIRW model with the vaccination to the newborn children. The stability of the SEIRW model with time-varying perturbation to predict the evolution tendency of the disease is analyzed. Furthermore, we introduce a time-varying delay into the susceptible and infective stages in the model and give some global exponential stability criteria for the time-varying delay system. Finally, numerical simulations are presented to verify the results.

Delay-dependent exponential stability criteria for neutral systems with interval time-varying delays and nonlinear perturbations

This paper investigates the problem of global exponential stability for neutral systems with interval time varying delays and nonlinear perturbations. It is assumed that the state delay belongs to a given interval, which means that both the lower and upper bounds of the time-varying delay are available. The uncertainties under consideration are norm-bounded. Based on the Lyapunov–Krasovskii stability theory, delay-partitioning technique and lower bounds lemma, less conservative delay-dependent exponential stability criteria are derived in terms of linear matrix inequalities (LMIs) with fewer decision variables than the existing ones. Numerical examples are given to show the effectiveness of the proposed method.

Phase Compensation Multiresonant Control of CVCF PWM Converters

In this paper, phase compensation is proposed for a multiple resonant control (MRSC) scheme to compensate system delays on the basis of phase compensation repetitive control (RC). The inherent relationship between RC and resonant control (RSC) is comprehensively developed: the partial equivalence between RC and MRSC, the advantages and disadvantages of MRSC over RC-much faster convergence rate at the cost of heavier parallel computation burden. Stability criterion of MRSC systems, zero-phase compensation at each harmonic frequency, and rules of thumb for choosing RSC gains are developed for synthesis of phase compensation MRSC. The proposed phase compensation scheme enables MRSC to independently choose compensation phase angle and control gain at each resonant frequency. Accurate phase compensations and optimal weighted control gains at each selected harmonic frequency enable MRSC systems to significantly improve the control performance: wide stability range, high tracking accuracy, and fast error convergence rate. Experimental results of a three-phase PWM inverter illustrate the validity of the phase compensation MRSC scheme.

Further improvement on delay-range-dependent stability results for linear systems with interval time-varying delays

This paper provides an improved delay-range-dependent stability criterion for linear systems with interval time-varying delays. No model transformation and no slack matrix variable are introduced. Furthermore, overly bounding for some cross term is avoided. The resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism, which is established theoretically. Finally, two numerical examples are given to show the effectiveness of the proposed results.

Delay‐dependent robust H ∞ filter design for uncertain neutral stochastic system with time‐varying delay

This study is concerned with the problem of the robust H ∞ filter design for uncertain neutral stochastic system with time-varying delay. With an appropriate augmented Lyapunov-Krasovskii functional formulated and a convex polyhedron method utilised, some novel delay-dependent exponential stability criteria for uncertain neutral stochastic system with time-varying delay are obtained in terms of linear matrix inequalities. Based on the obtained stability criteria, some sufficient conditions for the solvability of the robust H ∞ filter design are derived. The desired H ∞ filter is designed to guarantee the robustly exponential stability for the filtering error system with a prescribed H ∞ performance level. The novelty is that the desired results are obtained with less conservatism. Finally, two illustrative numerical examples are given to demonstrate the effectiveness of the authors obtained results.

Stability criterion for nonlinear systems

In the example of the Rossler model problem, a method for the practical analysis of the stability of nonlinear systems is considered. It is shown that besides the stability-instability conditions, the proposed criterion makes it possible in the analysis of the eigenvalue spectrum of the evolution matrix to determine the possibility of chaotic behavior of systems upon loss of stability.

A Convex Method of Robust Controller Design for Markovian Jump Systems with Uncertain Transition Rates

AbstractThis paper is concerned with exploring a convex controller design method for a class of Markovian jump systems with uncertain transition rates. First, a new stability criterion of such systems is established by applying the slack‐matrix technique. Then, a totally convex method for the state‐feedback controller design is derived in terms of linear matrix inequalities. The proposed design method has the merits of convexity and low conservativeness, while in the previous methods the two merits cannot coexist. Finally, a numerical example is given to illustrate the effectiveness and merits of the proposed method.

Improved delay-dependent stability criteria for continuous system with two additive time-varying delay components

This paper investigated the problem of improved delay-dependent stability criteria for continuous system with two additive time-varying delay components. Free weighting matrices and convex combination method are not involved, which achieves much less numbers of linear matrix inequalities (LMIs) and LMIs scalar decision variables. By taking advantage of integral inequality and new Lyapunov–Krasovskii functional, new less conservative delay-dependent stability criterion is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Stability analysis for discrete-time fractional-order LTI state-space systems. Part II: New stability criterion for FD-based systems

Abstract This paper presents a series of new results on the asymptotic stability of discrete-time fractional difference (FD) state space systems and their finite-memory approximations called finite FD (FFD) and normalized FFD (NFFD) systems. In Part I of the paper, new necessary and sufficient stability conditions have been given in a unified form for FD, FFD and NFFD-based systems. Part II offers a new, simple, ultimate stability criterion for FD-based systems. This gives rise to the introduction of new definitions of the so-called f-poles and f-zeros for FD-based systems, which are used in the closed-loop stability analysis for FD-based systems and, approximately, for FFD/NFFD-based ones

A Framework for Unconditional Stability Analysis of Multimaster/Multislave Teleoperation Systems

A novel robust stability analysis framework is presented for unconditional stability analysis of multimaster/multislave teleoperation systems. Unlike the unconditional stability criterion for single-user systems, the newly proposed criteria for unconditional stability of multimaster/multislave teleoperation systems depend on the multiport network parameters and the port terminations. In addition to the analytical solution, the graphical demonstration of the unconditional stability region facilitates the analysis of coupled stability against variations in the dynamics of the environments and operators, even when they behave actively. The proposed robust stability analysis framework is examined on two multilateral shared control architectures that were previously developed for dual-user teleoperation systems.

A Method for Deriving the Analytical Structure of a Broad Class of Typical Interval Type-2 Mamdani Fuzzy Controllers

Type-2 (T2) fuzzy controllers are emerging as the related T2 fuzzy logic, and algorithms have recently been advancing rapidly. At present, a T2 fuzzy controller is viewed and used as a black-box function generator that produces a desired nonlinear mapping between the input and output of the controller (we call the mapping analytical structure). The mathematical expression of the analytical structure, however, is not explicitly known to the controller designer. This is in sharp contrast with the analytical structure of a conventional controller, which is not only always explicitly known, but serves as a starting point for system analysis and design. Obviously, the knowledge of a T2 fuzzy controller's analytical structure can have significant benefits. They include 1) understanding more precisely how the controller works in the same sense as we understand how a conventional controller (e.g., the PID controller) functions; 2) making T2 fuzzy control more acceptable to safety-critical fields such as biomedicine; 3) taking advantage of the well-developed nonlinear control theory to develop better analysis and design methods for T2 control systems (e.g., less conservative system stability criteria); and 4) permitting rigorous comparative exploration on differences between the T2 and type-1 (T1) fuzzy controllers and their relative merits and pitfalls (e.g., performance and structural complexity). In this paper, we develop an innovative technique which is capable of deriving the analytical structure for a wide class of interval T2 Mamdani fuzzy controllers. The configuration of the controllers is typical and is substantially more general than the related efforts in the literature. It uses any number and types of interval T2 input fuzzy sets, any number and types of general or interval T2 output fuzzy sets, arbitrary fuzzy rules, Zadeh and operator, Karnik-Mendel center-of-sets type reducer, and the centroid defuzzifier. We show in detail how the derivation method works in a general setting and provide the analytical structure of an example T2 controller as well. In addition, we utilize the method to prove that a subset of the T2 fuzzy controllers are the sum of two nonlinear PI (or PD) controllers, each of which has a variable proportional gain and a variable integral gain (or derivative gain) plus a variable offset if and only if the input fuzzy sets are piecewise linear (e.g., triangular and/or trapezoidal). The sum of the two nonlinear PI (or PD) controllers is a new discovery relative to the current literature.