Stochastic Linear Time-varying Systems Research Articles

Optimal Fault Detection for Stochastic Linear Time-Varying Systems by $\chi ^{2}$ Test

Optimal Fault Detection for Stochastic Linear Time-Varying Systems by $\chi ^{2}$ Test

Annular Stochastic Finite-Time Stability Using Piecewise Quadratic Lyapunov Functions

In this letter we present some new sufficient conditions for the annular stochastic finite-time stability of a class of stochastic linear time-varying systems. These new conditions are obtained adopting time-varying piecewise quadratic Lyapunov functions rather than the classical quadratic ones. The proposed approach allows us to extend the class of consider domains, which are typically limited to ellipsoidal domains. The proposed finite-time stability conditions can be converted into a feasibility problem based on a set of differential linear matrix inequalities. Two numerical examples are considered to perform a comparison with the previous results, and they show that the new proposed conditions are less conservative than the previous ones.

Conditions for annular finite‐time stability of Itô stochastic linear time‐varing systems with Markov switching

In this study, the authors tackle some control problems related to the class of continuous-time, stochastic linear time-varying systems with Markov switching. First, the annular stochastic finite-time stability problem is considered, and two sufficient conditions are derived by considering the Ito formalism. Both conditions require the solution of a feasibility problem based on differential linear matrix inequalities. The former turns out to be less conservative and, therefore, is exploited in the analysis context; however, it cannot be converted into a computationally tractable condition for feedback purposes. The latter, which is based on a more conservative assumption, allows us to solve the state-feedback design problem. They show that the proposed approach obtains less conservative results with respect to the previous literature. Moreover, the application of the methodology to the finite-time control of a satellite illustrates the effectiveness of the proposed approach when facing engineering problems.

Robust detection of intermittent sensor faults in stochastic LTV systems

This paper addresses the detection problem of intermittent sensor faults for linear time-varying (LTV) systems with stochastic uncertainties. A robust filter is proposed which has advantages of zero mean and minimum state estimation error covariance. Then a corresponding residual generator is constructed and the quantitative influence of sensor faults on it is analyzed. Next, we design the evaluation function and detection threshold to achieve intermittent fault detection (IFD). Besides, the detectability of sensor faults is also provided. Finally, a simulation study is carried out to illustrate the effectiveness and applicability of our proposed method.

Annular finite-time stability analysis and synthesis of stochastic linear time-varying systems

In this paper, we investigate some finite-time control problems for stochastic linear time-varying systems, described by an Itô type differential equation. In particular, the annular stochastic finite-time stability control problem is dealt with. In this context, it is required that the norm of the state variables remains bounded between an inner and an outer ellipsoid, during a finite-interval of time. The first contribution of the paper consists of two sufficient conditions for stability, which are derived by exploiting an approach based on time-varying quadratic Lyapunov functions. The first condition requires the solution of two generalised differential Lyapunov equations; the latter the existence of a feasible solution to a pair of differential linear matrix inequalities. As particular cases, we obtain sufficient conditions for stochastic finite-time stability (in this last case, the lower ellipsoid collapses to the origin). From the analysis conditions, a sufficient condition is derived for the annular stochastic finite-time stabilisation via both state and output feedback. Some numerical examples illustrate the application of the proposed methodology and show that our approach attains less conservative results than those obtainable with the existing literature. Moreover, an application of the annular stochastic finite-time stability approach to the stabilisation problem of a satellite with respect to the geomagnetic field is presented.

Intermittent sensor fault detection for stochastic LTV systems with parameter uncertainty and limited resolution

ABSTRACT This paper considers the detection problem of intermittent sensor faults in stochastic linear time-varying systems with both parameter uncertainty and limited resolution. By introducing the soft measurement model, a state estimator is designed whose upper bound of estimation error covariance is obtained and minimised at each time step. Based on it, the residual is generated and its relationship with the fault is analysed quantitatively. Then the evaluation function and corresponding detection threshold is given. Our proposed method is recursive and therefore suitable for real-time online applications. At last, two simulation studies are carried out to illustrate the validity of our proposed method.

Optimal Control of Time-Varying Systems with Multiple Delays for Servo Appplications

We study the problem of optimal control of linear time-varying systems for servo applications and develop a generalized minimum variance controller for a multi-input and multi-output controlled autoregressive moving average model with multiple delays. The controller is applicable to a large class of stochastic linear time-varying systems regardless variation speed in plant parameters.

Residual Generation for Fault Diagnosis in Linear Time-Varying Systems

A residual generation method for fault diagnosis in deterministic and stochastic linear time-varying systems is proposed in this note. Based on appropriate assumptions on the monitored faults and on some persistent excitation condition, it enables complete diagnosis of any number of faults, regardless of the number of output sensors. In order to generate residuals for fault diagnosis, part of the possible faults are estimated with a recently developed technique of adaptive observer. The sensitivity of the residuals to the monitored faults is rigorously analyzed, as well as their insensitivity to the faults to be ignored.

Frequency-domain criterion for stability of stochastic linear time-varying systems

The objective of this paper is to extend the frequency domain critorion for predicting the stability of a clas9 of linear time-varying-gain systems, subject to white Gaussian noise input disturbance. It is shown that, if the noise is linearly related to the state of the system, a relatively simple frequency-domain inequality, that guarantees asymptotic stability with probability one (ASWPI) of the system, exists. The stochastic version of the second method of Lyapunov, along with a modified Moyer-Kalman-Yakubovich (M.K.Y.) lemma is used to derive such a condition. Finally geometric interpretation of the criterion is presented.