Filtering and fault estimation of descriptor switched systems

Abstract

International audienceIn this paper, the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to Lipschitz nonlinearities and unknown inputs (UI). The UI appear both on the dynamic and on the measurement equations. Two problems are addressed by L2-gain minimization with the use of switched Lyapunov functions and formulated by LMI. First, a functional observer for switched Lipschitz nonlinear descriptor system is proposed for robust state estimation. Second, fault estimation is performed by filtering the output estimation error, as usually done in the residual generation framework. Moreover, frequency weighting functions can be used to shape the response to the fault and thus improve the estimation

Recursive filtering adaptive fault‐tolerant tracking control for uncertain switched multivariable nonlinear systems

“…The control problem of Van der Pol oscillator that can represent various types of electrical circuits consisting of resisters, inductance coils a capacitor, and a triode with two DC power sources. 53 The balance equation of the switched nonlinear system is described as below: In the simulation, the actuator faults are chosen as u 2 = 1 during t ∈ (10,50] and u 2 = e −0.1t during t ∈ (50, 60], u 1 = 0.9u 1 during t ∈ (25,40], u 3 = 3 during t ∈ (40,60]. The tracking command is r(t) = sin(0.4t).…”

Robust fault estimation based on zonotopic Kalman filter for discrete‐time descriptor systems

“…where ∈ ℝ (p−q)×p is an arbitrary matrix guaranteeing that Ω has full-row rank andḠ(k) ∈ ℝ n×(p−q) . Besides,Ḡ(k) = G * (k) minimizes J = tr(WP(k + 1)) with P(k + 1) in (23), which is computed through the following procedure:…”

“…Robust fault estimation approaches for linear descriptor systems can be found in other works . Besides, the fault estimation approaches have also studied for linear parameter‐varying systems and switched descriptor systems . Among these approaches, the estimated fault results are obtained as punctual values.…”

“…8,17,18 Besides, the fault estimation approaches have also studied for linear parameter-varying systems [19][20][21][22] and switched descriptor systems. 23 Among these approaches, the estimated fault results are obtained as punctual values. Alternatively, set-based approaches have been established for state estimation 24,25 and for fault diagnosis and fault-tolerant control.…”

Finite‐time boundedness and stabilisation of switched linear systems using event‐triggered controllers

“…As an important class of hybrid systems [15, 16], switched systems have been a hot topic in the field of control theory and applications, and a number of important results have been reported, see a survey [17] and some recent results including stability and stabilisation issues [18–20], switched non‐linear systems [21, 22], switched time‐delay systems [23–25], filter design [26, 27], iterative learning control [28] and asymptotic stability under sampled‐data and quantisation [29]. However, if an event‐triggering scheme is introduced into switched systems, how to guarantee the desired performance of the closed‐loop systems, though a fundamentally important problem, has not been fully addressed yet.…”