Robust fault‐tolerant control for uncertain delta operator switched systems

Abstract

This study addresses two issues of robust fault-tolerant stabilisation with circular disk pole constraints for uncertain delta operator switched systems with actuator faults. The first computes the dwell time and proposes a state feedback controller design approach to stabilise the considered switched system. The second solves the D-stabilisation problem based on state switching strategy. Finally, an illustrative example is provided to validate the feasibility and effectiveness of the proposed approaches. Nomenclature Rset of real numbers R n set of n-dimensional real column vectors R m×n set of m × n real matrices δ delta operator D an LMI region D(q, r) circular disk with centre at (−q, 0) and radius r, where q, r ∈ R and r > 0; If A, B ∈ R n×n , then He(A) denotes the matrix A + A T A( ) < 0 denotes that the matrix A is a negative (semi-) definite symmetric matrix A( ) < B denotes that the matrix A − B is a negative (semi-) definite symmetric matrix

Robust control for a class of non‐linear discrete time‐delay systems with controller failure: a probability‐dependent method

“…Step 2: If step 1 holds, substituting δ 1 and δ 2 into (15) and (16), one can seek the feasible solutions to (15) and (16). Remark 7: For a switched system with stable and unstable subsystems, the stability conditions given by the existing results often require that the activation time ratio between the stable system and unstable system is not less than a specified constant depending on α and β.…”

“…On the other hand, controller failure problem has been extensively investigated in the past few decades [13][14][15][16][17][18][19][20][21]. As pointed out in [17], controller failure is often encountered in engineering applications due to various reasons, for example control signal cannot be perfectly transmitted in the network control [13,14].…”

“…As pointed out in [17], controller failure is often encountered in engineering applications due to various reasons, for example control signal cannot be perfectly transmitted in the network control [13,14]. Actuator may go wrong in fault-tolerant control [15,16], or the controller itself is unavailable sometimes for some environmental or purposeful factors [17][18][19][20] and so on. The temporary failure of a controller is referred to a short complete breakdown in its operation and can resume normal working after a time interval, and exponential stability conditions for such systems were derived in [17][18][19][20].…”

Asymptotic tracking and dynamic regulation of SISO non‐linear system based on discrete multi‐dimensional Taylor network

“…It promises a guaranteed cost controller with quadratic stability, if and only if there exists a matrix K and a positive definite symmetric matrixX = P −1 to ensure the matrix inequality (22), in the case of all admissible uncertain parameters [36] −X X + hĀ δ X * −X + X(hQ + hK T RK)X < 0 (22) where Ā δ is the state matrix of the closed-loop system (18). From (19) and Lemma 1 of [37], (22) is equivalent to…”

“…In terms of Lemma 1 of [37] and Schur complement lemma, (26) is equivalent to (25). □ By Propositions 1 and 2, the procedure of the controller design is given as follows:…”