Xu-Guang Li

Stability analysis of neutral systems with distributed delays.

Abstract The stability of neutral systems with distributed delays is investigated in this paper. A modified Lyapunov–Krasovskii functional is constructed to study this class of systems. The proposed stability criterion is discrete-, distributed- and neutral-delay-dependent. In addition, by this method one can study the case when the coefficient matrix of the neutral delay term is time-varying uncertain. The reduced conservatism is illustrated in a numerical example.

Technical communique: Stability analysis of neutral systems with mixed delays

The stability of neutral systems with mixed delays is studied in this paper. A new discretized Lyapunov functional method is proposed. The method in this paper is less conservative than the existing ones and the results are very close to the analytical results. In addition, this method allows the coefficient matrix of the neutral term to have time-varying uncertainties.

Some problems in the stability of networked-control systems with periodic scheduling

This article addresses three stability problems related to networked-control systems (NCSs) with periodic scheduling, where control systems may have multiple samplings in a hyperperiod (a hyperperiod is a periodically repeated scheduling sequence for all tasks in an NCS). As expected, the analysis of a system with multiple samplings is much richer than the case with single sampling. For example, a system with two samplings may be stable (unstable) even if it is unstable (stable) when sampled by either sampling. In this context, it is important to understand how network-induced delays and multiple samplings affect the systems stability. In this article, three particular stability problems involving constant and/or time-varying parameters are investigated, and the corresponding stability regions are derived. Numerical examples and various discussions complete the presentation.

Stability analysis of networked control systems based on a switched control

Abstract This paper studies the stability of networked control systems with a switched control law. Both the cases of constant and time-varying sampling periods are considered and the stability intervals are obtained. It is seen that this method can lead to bigger stability intervals than the standard control law. In particular, some NCSs can be stabilized with an infinitely big sampling period. A sufficient condition for this case is presented.

On τ-Decomposition Frequency-Sweeping Test for a Class of Time-Delay Systems. Part II: Multiple Roots Case

Abstract This paper addresses the stability analysis problem of a class of linear system with commensurate delays in a frequency-domain setting. In Part I of this paper, only the simple imaginary roots (SIRs) case is considered. In Part II of the paper, the case of multiple imaginary roots (MIRs) will be studied and general results on the issues of Puiseux series expansion, invariance, and instability persistence will be presented. By the approach proposed in this two-part paper, we can study the complete stability for the time-delay systems under consideration.

Some remarks on robust stability of networked control systems

This paper focuses on the robust stability of networked control systems (NCSs), considering time-delay and sampling period simultaneously. Particular stability problems involving constant and/or time-varying parameters are investigated, and the corresponding stability regions are derived. The methods are based on searching an appropriate Lyapunov matrix and parameter-sweeping. It is shown that the obtained results are less conservative than the existing ones.

Optimization for networked control systems under the hyper-sampling period

The hyper-sampling mode was recently proposed and studied in the community of networked control systems (NCSs). Compared with its widely-used single-sampling counterpart, the hyper-sampling mode brings a more flexible sampling mechanism. However, the relation between the dynamic performance of the NCS and the hyper-sampling period has not been fully investigated so far. The objective of this paper is to study how to design the hyper-sampling sequence such that: under a given average sampling frequency, the system dynamic performance is optimal. The approach is based on the analytic relation between the performance index and the hyper-sampling period and a parameter-sweeping technique. As a byproduct of the prosed approach, we may optimize the feedback gain matrix of an NCS using the similar idea.

Complete stability of linear time-delay systems: A new frequency-sweeping frequency approach

The complete stability of time-delay systems (TDSs) has not been fully investigated so far, though this issue has attracted considerable attention. In order to systematically solve this problem, we need to study two critical properties: the invariance and the ultimate stability properties. In this paper, we present a new frequency-sweeping approach, by using which we can prove the invariance property and then find the ultimate stability condition for the first time. In addition, we will show that the proposed frequency-sweeping framework is a unified approach. We can obtain the complete stability of a TDS by only performing the frequency-sweeping test.

Optimal Design of Distributed Control and Embedded Systems

Optimal Design of Distributed Control and Embedded Systems focuses on the design of special control and scheduling algorithms based on system structural properties as well as on analysis of the influence of induced time-delay on systems performances. It treats the optimal design of distributed and embedded control systems (DCESs) with respect to communication and calculation-resource constraints, quantization aspects, and potential time-delays induced by the associated communication and calculation model. Particular emphasis is put on optimal control signal scheduling based on the system state. In order to render this complex optimization problem feasible in real time, a time decomposition is based on periodicity induced by the static scheduling is operated. The authors present a co-design approach which subsumes the synthesis of the optimal control laws and the generation of an optimal schedule of control signals on real-time networks as well as the execution of control tasks on a single processor. The authors also operate a control structure modification or a control switching based on a thorough analysis of the influence of the induced time-delay system influence on stability and system performance in order to optimize DCES performance in case of calculation and communication resource limitations. Although the richness and variety of classes of DCES preclude a completely comprehensive treatment or a single best method of approaching them all, this co-design approach has the best chance of rendering this problem feasible and finding the optimal or some sub-optimal solution. The text is rounded out with references to such applications as car suspension and unmanned vehicles. Optimal Design of Distributed Control and Embedded Systems will be of most interest to academic researchers working on the mathematical theory of DCES but the wide range of environments in which they are used also promotes the relevance of the text for control practitioners working in the avionics, automotive, energy-production, space exploration and many other industries.

On τ-Decomposition Frequency-Sweeping Test for a Class of Time-Delay Systems. Part I: Simple Imaginary Roots Case

Abstract This paper addresses the stability analysis problem of a class of linear system with commensurate delays in a frequency-domain setting. In Part I of this paper, only the simple imaginary roots (SIRs) case is considered. First, the characteristic quasipolynominal is reformulated into a factorization form. Then, it is found that (i) the crossing direction of imaginary roots (CDIRs) can be reflected by an appropriate frequency-sweeping test, (ii) the CDIRs are determined by a certain order of the imaginary roots by magnitude and finally, (iii) a time-delay system is ultimately unstable if there is at least one crossing imaginary root. To apply the properties (i)-(iii), an easily implemented frequency-sweeping method is proposed, by which the CDIRs can be obtained without any further computation. The method can be used for the complete stability of the system. In Part II of the paper, the MIR case will be discussed.