A NEW METHOD FOR FINDING THE NATURAL FREQUENCY SET OF A LINEAR TIME-INVARIANT NETWORK

This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the common equation the natural frequencies of an n th order network are correlated with the n port parameters. The equation is simple and dual in form and clear in its physical meaning. The procedure of finding the solution is simplified and standardized, and it will not cause the loss of roots. The common equation would find wide use and be systematized.

Compressive Measurement Identification of Linear Time-Invariant System Application in DC Motor

In traditional system identification (SI), actual values of system parameters are concealed in the input and output data;hence, it is necessary to apply estimation methods to determine the parameters. In signal processing, a signal with N elements must be sampled at least N times. Thus, most SI methods use N or more sample data to identify a model with N parameters;however, this can be improved by a new sampling theory called compressive sensing (CS). Based on CS, an SI method called compressive measurement identification (CMI) is proposed for reducing the data needed for estimation, by measuring the parameters using a series of linear measurements, rather than the measurements in sequence. In addition, the accuracy of the measurement process is guaranteed by a criterion called the restrict isometric principle. Simulations demonstrate the accuracy and robustness of CMI in an underdetermined case. Further, the dynamic process of a DC motor is identified experimentally, establishing that CMI can shorten the identification process and increase the prediction accuracy.

Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems

In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

FUZZY ROBUST H_∞ CONTROL OF UNCERTAIN NONLINEAR SYSTEM WITH TIME-DEALY

This paper addresses the problem of the fuzzy H ∞state feedback control for a class of uncertain nonlinear systems with time delay. The Takagi Sugeno (T S) mo del with time delay and parameter uncertainties is adopted for modeling of nonlinear system. The systematic design procedure for the fuzzy robust controller based on linear matrix inequality (LMI) is given. Some sufficient conditions are derived for the existence of fuzzy H ∞ state feedback controllers such that the closed loop system is asymptotically stable and the effect of the disturbance input on controlled output is reduced to a prescribed level. An example is given to demonstrate the effectiveness of the proposed method.

Equilibrium Control Theory and Direct Method of Feedback Linearization for Nonlinear Time Varying Systems

Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.

FIXED-DESIGN SEMIPARAMETRIC REGRESSION FOR LINEAR TIME SERIES

This article studies parametric component and nonparametric component estimators in a semiparametric regression model with linear time series errors; their r-th mean consistency and complete consistency are obtained under suitable conditions. Finally, the author shows that the usual weight functions based on nearest neighbor methods satisfy the designed assumptions imposed.

Impact angle control over composite guidance law based on feedback linearization and finite time control

The impact angle control over guidance(IACG) law against stationary targets is proposed by using feedback linearization control(FLC) and finite time control(FTC). First, this paper transforms the kinematics equation of guidance systems into the feedbackable linearization model, in which the guidance law is obtained without considering the impact angle via FLC. For the purpose of the line of sight(LOS) angle and its rate converging to the desired values, the second-order LOS angle is considered as a double-integral system. Then, this paper utilizes FTC to design a controller which can guarantee the states of the double-integral system converging to the desired values. Numerical simulation illustrates the performance of the IACG, in contrast to the existing guidance law.

FIXED-DESIGN REGRESSION FOR LINEARTIME SERIES

This paper obtains asymptotic normality for double array sum of linear time series zeta(t), and gives its application in the regression model. This generalizes the main results in [1].

Minimum Dwell Time for Global Exponential Stability of a Class of Switched Positive Nonlinear Systems

This paper will investigate global exponential stability analysis for a class of switched positive nonlinear systems under minimum dwell time switching, whose nonlinear functions for each subsystem are constrained in a sector field by two odd symmetric piecewise linear functions and whose system matrices for each subsystem are Metzler. A class of multiple time-varying Lyapunov functions is constructed to obtain the computable sufficient conditions on the stability of such switched nonlinear systems within the framework of minimum dwell time switching.All present conditions can be solved by linear/nonlinear programming techniques. An example is provided to demonstrate the effectiveness of the proposed result.

Critical dwell time of switched linear systems

In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable （While some switching models are probably unstabilizable）, an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition, algorithms for designing switching laws and controls are presented.

The improved local linear prediction of chaotic time series

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

High-precision and wide-range real-time neutron flux monitor system through multipoint linear calibration

The neutron flux monitor(NFM)system is an important diagnostic subsystem introduced by large nuclear fusion devices such as international thermonuclear experimental reactor(ITER),Japan torus-60,tokamak fusion test reactor,and HL-2 A.Neutron fluxes can provide real-time parameters for nuclear fusion,including neutron source intensity and fusion power.Corresponding to different nuclear reaction periods,neutron fluxes span over seven decades,thereby requiring electronic devices to operate in counting and Campbelling modes simultaneously.Therefore,it is crucial to design a real-time NFM system to encompass such a wide dynamic range.In this study,a high-precision NFM system with a wide measurement range of neutron flux is implemented using realtime multipoint linear calibration.It can automatically switch between counting and Campbelling modes with variations in the neutron flux.We established a testing platform to verify the feasibility of the NFM system,which can output the simulated neutron signal using an arbitrary waveform generator.Meanwhile,the accurate calibration interval of the Campbelling mode is defined well.Based on the above-mentioned design,the system satisfies the requirements,offering a dynamic range of 10~8 cps,temporal resolution of 1 ms,and maximal relative error of 4%measured at the signal-to-noise ratio of 15.8 dB.Additionally,the NFM system is verified in a field experiment involving HL-2 A,and the measured neutron flux is consistent with the results.

FINITE TIME BLOW UP OF THE SOLUTIONS TO BOUSSINESQ EQUATION WITH LINEAR RESTORING FORCE AND ARBITRARY POSITIVE ENERGY

Finite time blow up of the solutions to Boussinesq equation with linear restoring force and combined power nonlinearities is studied. Sufficient conditions on the initial data for nonexistence of global solutions are derived. The results are valid for initial data with arbitrary high positive energy. The proofs are based on the concave method and new sign preserving functionals.

Effects of time delay on stochastic resonance of a periodically driven linear system with multiplicative and periodically modulated additive white noises

Stochastic resonance （SR） of a periodically driven time-delayed linear system with multiplicative white noise and periodically modulated additive white noise is investigated. In the condition of small delay time, an approximate analytical expression of output signal-to-noise ratio （SNR） is obtained. The analytical results indicate that （1） there exists a resonance peak in the curve for SNR versus time delay; （2） the time delay will suspend the SR dramatically for SNR versus other parameters of the system, such as noise intensity, correlation intensity, and signal frequency, once a certain value is reached, the SR phenomenon disappears.

Novel Adaptive Learning Control of Linear Systems with Completely Unknown Time Delays

A novel output-feedback adaptive learning control approach is developed for a class of linear time-delay systems. Three kinds of uncertainties： time delays, number of time delays, and system parameters are all assumed to be completely unknown, which is dfferent from the previous work. The design procedure includes two steps. First, according to the given periodic desired reference output and the allowed bound of tracking error, a suitable finite Fourier series expansion （FSE） is chosen as a practical reference output to be tracked. Second, by expressing the delayed practical reference output as a known time-varying vector multiplied by an unknown constant vector, we combine three kinds of uncertainties into an unknown constant vector and then estimate the vector by designing an adaptive law. By constructing a Lyapunov-Krasovskii functional, it is proved that the system output can asymptotically track the practical reference signal. An example is provided to illustrate the effectiveness of the control scheme developed in this paper.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

Hyers-Ulam Stability of First Order Nonhomogeneous Linear Dynamic Equations on Time Scales

This paper deals with the Hyers-Ulam stability of the nonhomogeneous linear dynamic equation x~?(t)-ax(t) = f(t), where a ∈ R^+. The main results can be regarded as a supplement of the stability results of the corresponding homogeneous linear dynamic equation obtained by Anderson and Onitsuka(Anderson D R, Onitsuka M. Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales. Demonstratio Math., 2018, 51: 198–210).

Finite-time Control of Linear Singular Systems with Parametric Uncertainties and Disturbances

The concept of finite-time stability for linear singular system is induced in this paper.Finite-time control problem is considered for linear singular systems with time-varying parametricuncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with para-metric uncertainties. A su?cient condition is presented for robust finite-time stabilization via statefeedback. The condition is translated to a feasibility problem involving restricted linear matrix in-equalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities.Finally, an example is given to show the validity of the results.

Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.