Observer-Based Bounded Control for Discrete Time-Delay Uncertain Nonlinear Systems

Hindawi Publishing Corporation Discrete Dynamics in Nature and Society Volume 2015, Article ID 135248, 16 pages http://dx.doi.org/10.1155/2015/135248 Research Article Observer-Based Bounded Control for Discrete Time-Delay Uncertain Nonlinear Systems Bei Wu,1,2 Mou Chen,1,3 and Xiaoming Chen1,3 1 College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China Nanhang Jincheng College, Nanjing, Jiangsu 211156, China 3 Jiangsu Key Laboratory of Internet of Things and Control Technologies, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016, China 2 Correspondence should be addressed to Mou Chen; Received 1 September 2015; Accepted 21 October 2015 Academic Editor: Chenguang Yang Copyright © 2015 Bei Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A bounded controller is proposed for a class of uncertain discrete time-delay systems with nonlinearity and disturbance based on state estimator and disturbance observer technique. A state estimator is developed to estimate the unmeasured system state vector. Suppose that the disturbance is generated by an exogenous system; a disturbance observer is designed to estimate the unknown disturbance. The parameters of the state estimator and the disturbance observer are calculated by solving linear matrix inequalities (LMIs). By applying the outputs of the state estimator and the disturbance observer, the sufficient condition for the existence of the bounded controller is derived based on an appropriate Lyapunov function candidate. Under the developed bounded controller, the stability of the closed-loop system can be guaranteed. Simulation examples are provided to show the effectiveness of the proposed bounded control scheme. 1. Introduction Time-delay phenomenon widely exists in most of industrial systems, such as biological systems, hydraulic systems, transmission systems, electrical networks, and chemical systems [1–5]. The existence of time-delay leads to performance degradation or even system instability and causes the complication to the analysis and design of the controller. Up to now, many control schemes have been studied for timedelay systems, such as guaranteed cost control [1], 𝐻∞ control [2, 4], adaptive neural network control [5, 6], sliding mode control [7, 8], and disturbance-observer-based control [9–14]. However, most of the above-mentioned research results are dealing with continuous-time systems. Due to the fast development of computers and digital signal processor (DSP) chips, considerable attention has been paid to the study of discrete time-delay systems [15, 16]. The stability control problem of discrete time-delay systems can be divided into delay-dependent stability control [17–19] and delayindependent stability control [20]. Since delay-dependent conditions are less conservative than delay-independent conditions, more concentrations have been given on the delay dependent stability analysis. Usually, the model errors, the measurement errors, and the external disturbances inevitably exist in dynamic systems, which can also further cause the degradation of system performance and even instability. The problem of robust stability analysis and robust controller design has been extensively studied for discrete-time systems with uncertainty and/or disturbance. A novel adaptive-critic-based neural network (NN) controller was proposed for nonlinear singleinput-single-output (SISO) discrete-time systems in [21]. The novel adaptive control technique was proposed for discretetime multi-input-multi-output (MIMO) systems in [22]. The improved dynamic surface control design was studied for constrained hypersonic flight models in [23]. In [24], based on the key ideas of “future outputs prediction” and “nearest-neighbour compensation,” the adaptive predictive control laws were developed for nonlinear autoregressive moving average systems. In [25], the problem of robust 2 stabilization was investigated for discrete-time singular largescale systems with time-invariant norm-bounded uncertainties. Based on the dynamic surface control technique, both indirect and direct global neural controllers were developed for the strict-feedback systems in [26]. In [27], the output feedback adaptive neural network controllers were developed for nonlinear discrete-time systems. The output feedback adaptive control technique was investigated for discrete-time systems with unknown control directions in [28]. In [29], a robust adaptive sliding mode controller was constructed for discrete time-delay systems with mismatched uncertainties and matched external disturbances. Since the disturbances widely exist in practical systems and most of them are difficult to be measured, many advanced control approaches, such as adaptive control and sliding mode control, have been proposed. However, the control approaches mentioned above are rejecting disturbances via feedback control based on the tracking error, which can not deal with strong disturbances directly and fast [30]. Then, the disturbance observer was proposed to estimate unmeasured disturbances for engineering application systems such as direct-current servomotor systems [31], robotic manipulators [32], and data storage systems [33]. A reduced order disturbance observer was studied for discrete-time linear systems in [33]. Based on the disturbance observer, an antidisturbance controller was investigated for discrete time-varying delay systems with multiple disturbances under actuator failures in [34]. In [35], disturbance-observer-based control and 𝐻∞ control were discussed for A4D aircraft at a flight condition of 15000 ft altitude and 0.9 Mach, the states were made up with the forward velocity, the angle of attack, the pitching velocity, and the pitching angle, and the state delay was considered. A composite fuzzy control was investigated for uncertain nonlinear systems based on the disturbance observer technique in [36]. However, the input time-delay was seldom considered in the research results mentioned above. Time delay in control inputs brings new challenges in the controller design. The problem of 𝐻∞ control was investigated for discrete time-varying input-delay systems via Riccati difference equation in [37]. In [38], the state feedback prediction-based control law was developed for a discrete-time system with input time-varying delay. Applying Artstein’s reduction method and the scaled bounded real lemma, a sufficient condition was presented to stabilize linear discrete-time systems with time-varying input delay and model uncertainties in [39]. In [40, 41], the guaranteed cost control problem was studied for a class of discrete timedelay systems via state feedback. The problem of multiple input delays was discussed in [42]. A robus (...truncated)