Robust Finite‐Time Control for Linear Time‐Varying Delay Systems With Bounded Control

Abstract

This paper develops a novel finite-time control design for linear systems subject to time-varying delay and bounded control. Based on the Lyapunov-like functional method and using a result on bounding estimation of integral inequality, we provide some sufficient conditions for designing state feedback controllers that guarantee the robust finite-time stabilization with guaranteed cost control. The conditions are obtained in terms of linear matrix inequalities (LMIs), which can be determined by utilizing the Matlab LMI Control Toolbox. A numerical example is given to show the effectiveness of the proposed method.whereM 12,12 = −0.5I, M 10,10 = − 1 1 + 27r 2 b 4 I, M 44 = −8S 3 + Q 2 , M 11,11 = − 1 , M 88 = M 99 = −12S 3 , M 12 = −2X 1 , M 13 = −2X 2 , M 14 = PD, M 16 = 6X 1 , M 45 = D T S 4 , M 1i = 0, i = 8, 9, 12, M 1,10 = P, M 1,11 = PB, M 15 = A ⊤ S 4 , M 24 = −2S 3 , M 26 = 6X 1 , M 28 = 6S 3 , M 2i = 0, i = 3, 5, 7, 9, 10, 11, 12, M 34 = −2S 3 , M 39 = 6S 3 , M 3i = 0, i = 5, 6, 8, 10, 11, 12, M 4i = 0, i = 6, 7, 10, 11, 12, M 48 = M 49 = 6S 3 , M 5i = 0, i = 6, 7, 8, 9, 10, 11, M 5,12 = S 4 ,

LMI-Based Robust Stabilization of a Class of Input-Constrained Uncertain Nonlinear Systems with Application to a Helicopter Model

“…us, the neglect of the actuator constraints in the controller design may cause instability of the closed-loop system [17][18][19]. e design of controllers for continuous-time and discrete-time systems by taking into consideration the actuator saturation has been extensively studied in the past few decades [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Some works have investigated the problem of uncertainties and actuator saturation in mechatronic systems such as the vehicle lateral dynamics [37], the vehicle active suspension systems [38][39][40][41], the rigid spacecraft [42,43], the inertia wheel inverted pendulum [12], the supercavitating vehicle [44], the flexible robotic manipulator [45], and the marine surface vessel [46], among others.…”

Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations

“…However, in practical applications, synchronization is always expected to be achieved as fast as possible. Moreover, compared with asymptotic synchronization, finite‐time synchronization is optimal and has many advantages . It is worth mentioning that the models in did not consider time delays.…”

“…Moreover, compared with asymptotic synchronization, finite‐time synchronization is optimal and has many advantages . It is worth mentioning that the models in did not consider time delays. Actually, in real world, due to finite speed of switching of amplifiers and transmission of signals in hardware implementation, time delays are unavoidable in NNs.…”

Finite‐Time Scaled Consensus in Discrete‐Time Networks of Agents

“…Finite‐time convergence has also been considered as one of the most important performance indicators for the design of consensus algorithms (see e.g. ). In this brief paper, we show that finite‐time scaled consensus can always be achieved for connected bidirectional graphs via linear iterations in a distributed fashion.…”