Finite-time stability for switched singular systems

Abstract

In this paper, finite-time stability and stabilization of switched singular systems are studied. Firstly, we discuss the solvability condition of the switched singular system and introduce the concepts of finite-time stability and finite-time boundness. Secondly, using the mode-dependent average dwell time method and the Lyapunov function method, we provide sufficient conditions to guarantee that the switched singular system is regular, impulse free, and finite-time stable or finite-time bounded. Then, we design the state feedback controllers to ensure that a closed-loop system is finite-time stable and finite-time bounded with a present H disturbance attenuation level . Finally, numerical examples are given to verify the efficiency of the proposed theory.

Robust iterative learning control for random switched singular systems in time domain

“…From Figures 4and 5 and 8 and 9, it can be seen that when the fixed gain iterative learning control algorithm is adopted for switched singular systems with measurement noises, the state curve gradually approaches the desired trajectory with the increase of the number of iterations, while the effect of measurement noises does not change. However, it can be seen from Figures 6 and 7 and 10 and 11 that when using the robust iterative learning control algorithm (6) designed in this paper, not only the system state can gradually approach the desired trajectory with the increase of the number of 2) via the fixed gain iterative learning algorithm at 160th iteration. Figure 6.…”

“…k (t), where x (1) k (t), x (2) k (t) are the states without noise disturbance, d (1) k (t) and d (2) k (t) are the measurement noise of x (1) k (t) and x (2) k (t), respectively. Denote state tracking errors are e 1k (t) = x (1) d (t) À x (1) k (t) and e 2k (t) = x (2) d (t) À x (2) k (t), where x (1) d (t) and x (2) d (t) are the desired states, while actual measurement errors are e 1k (t) = x (1) d (t) À x (1) m, k (t), e 2k (t) = x (2) d (t) À x (2) m, k (t). So we can know e 1k (t) = e 1k (t) À d (1) k (t), e 2k (t) = e 2k (t) Àd (2) k (t).…”

“…Denote state tracking errors are e 1k (t) = x (1) d (t) À x (1) k (t) and e 2k (t) = x (2) d (t) À x (2) k (t), where x (1) d (t) and x (2) d (t) are the desired states, while actual measurement errors are e 1k (t) = x (1) d (t) À x (1) m, k (t), e 2k (t) = x (2) d (t) À x (2) m, k (t). So we can know e 1k (t) = e 1k (t) À d (1) k (t), e 2k (t) = e 2k (t) Àd (2) k (t).…”

“…Tracking effect of x (1) via this algorithm at 40th iteration. (2) via this algorithm at 40th iteration.…”

“…Figure 9. Tracking effect of x(2) via the fixed gain iterative learning algorithm at 160th iteration. Figure6.…”