The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for...The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.展开更多
In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncer...In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.展开更多
For flight control systems with time-varying delay, an H∞ output tracking controller is proposed. The controller is designed for the discrete-time state-space model of general aircraft to reduce the effects of uncert...For flight control systems with time-varying delay, an H∞ output tracking controller is proposed. The controller is designed for the discrete-time state-space model of general aircraft to reduce the effects of uncertainties of the mathematical model, external disturbances, and bounded time-varying delay. It is assumed that the feedback-control loop is closed by the communication network, and the network-based control architecture induces time-delays in the feedback information. Suppose that the time delay has both an upper bound and a lower bound. By using the Lyapu- nov-Krasovskii function and the linear matrix inequality （LMI）, the delay-dependent stability criterion is derived for the time-delay system. Based on the criterion, a state-feedback H∞ output tracking controller for systems with norm-bounded uncertainties and time-varying delay is presented. The control scheme is applied to the high incidence research model （HIRM）, which shows the effectiveness of the proposed approach.展开更多
This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. Th...This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler＇s lemma and Dualization lemma, some novel conditions for exponential H∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities （LMIs）, which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.展开更多
In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer m...In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer matrices. Initial conditions and cross-correlated uncertainty inputs are described by the sum quadratic constraint （SQC）. Without modifying the SQC, the minimal state of the SQC is obtained through Krein space method. The inertia condition for a minimum of a deterministic quadratic form is derived when the coefficient of observer uncertainty input is non-unit matrix. Recursions of Krein space state filtering and bias filtering are developed respectively. Since the cross correlation between uncertainties is considered, a cross correlation gain is introduced into the posteriori estimator. Finally, a numerical example illustrates the performance of the proposed filter.展开更多
基金supported by Research Foundation of Education Bureau of Shannxi Province, PRC(No.2010JK400)
文摘The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality （LMI） approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the effectiveness of the proposed approach.
基金supported by the National Natural Science Foundation of China (Grant No. 52105253)the State Key Program of National Science Foundation of China (Grant No.52235005)。
文摘In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.
基金supported by the National Natural Science Foundation of China (Nos:61074027 and 61273083)
文摘For flight control systems with time-varying delay, an H∞ output tracking controller is proposed. The controller is designed for the discrete-time state-space model of general aircraft to reduce the effects of uncertainties of the mathematical model, external disturbances, and bounded time-varying delay. It is assumed that the feedback-control loop is closed by the communication network, and the network-based control architecture induces time-delays in the feedback information. Suppose that the time delay has both an upper bound and a lower bound. By using the Lyapu- nov-Krasovskii function and the linear matrix inequality （LMI）, the delay-dependent stability criterion is derived for the time-delay system. Based on the criterion, a state-feedback H∞ output tracking controller for systems with norm-bounded uncertainties and time-varying delay is presented. The control scheme is applied to the high incidence research model （HIRM）, which shows the effectiveness of the proposed approach.
基金Supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region of China under Project CityU/112907
文摘This paper investigates the problem of robust exponential H∞ static output feedback controller design for a class of discrete-time switched linear systems with polytopic-type time-varying parametric uncertainties. The objective is to design a switched static output feedback controller guaranteeing the exponential stability of the resulting closed-loop system with a minimized exponential H∞ performance under average dwell-time switching scheme. Based on a parameter-dependent discontinuous switched Lyapunov function combined with Finsler＇s lemma and Dualization lemma, some novel conditions for exponential H∞ performance analysis are first proposed and in turn the static output feedback controller designs are developed. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities （LMIs）, which are numerically efficient with commercially available software. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approaches.
基金supported by the Fundamental Research Funds for the Central Universities(No.DL13BB14)
文摘In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer matrices. Initial conditions and cross-correlated uncertainty inputs are described by the sum quadratic constraint （SQC）. Without modifying the SQC, the minimal state of the SQC is obtained through Krein space method. The inertia condition for a minimum of a deterministic quadratic form is derived when the coefficient of observer uncertainty input is non-unit matrix. Recursions of Krein space state filtering and bias filtering are developed respectively. Since the cross correlation between uncertainties is considered, a cross correlation gain is introduced into the posteriori estimator. Finally, a numerical example illustrates the performance of the proposed filter.
