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This paper addresses the problem of the H ∞ analysis of positive continuous systems with time-delay. The corresponding bounded real lemma is newly characterized in terms of linear matrix inequalities, in which Lyapunov matrix can be diagonal. Based on the separation theorem of convex set in Euclidean space, we prove that the delay size has no influence on the bounded real lemma of such systems.

In this paper, we are concerned with H ∞ model reduction of 2-D discrete systems in Roesser model. For positive 2-D discrete systems, the aim is to construct a positive 2-D reduced-order system such that the error system satisfies a prescribed H ∞ norm bound constraint. Based on a system augmentation approach, a new sufficient condition is proposed to ensure that the error system is stable and satisfies a prescribed H ∞ norm. Then the existence condition of the reduced-order system matrixes are given and an corresponding iterative linear matrix inequality(LMI) algorithm is presented. Finally, a numerical example to illustrate the effectiveness of the proposed design procedures is presented.

This paper addresses the design of positive observer for positive linear continuous system with interval uncertainties and multiple time-delay. Firstly, the sufficient and necessary condition for the existence of positive observers is established by using the vertical matrices of the uncertain domain which system matrices belong to. Then the desired observer matrices are given by solving a set of matrix inequalities. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.

This paper investigates the problem of the robust delay-dependent stability for uncertain stochastic systems with interval time-varying delays. By establishing a new Lyapunov function and using the convex function theory, the delay-dependent sufficient criteria is derived in terms of linear matrix inequalities (LMIs), which takes into account the range of the upper and lower bound of interval time-varying delays. A numerical example is given to illustrate the effectiveness of the proposed method.

The problem of robust strictly passive analysis for a class of uncertain discrete singular time-delay systems is investigated in this paper. The discrete singular systems under consideration involve constant time-delay and norm-bounded uncertainties. Based on an integral inequality, a new sufficient condition is firstly obtained, which guarantees that the discrete singular time-delay systems are admissible and strictly passive. Meanwhile, the sufficient condition for robust strictly passive is also obtained in terms of linear matrix inequality (LMI). A numerical example is also given to demonstrate the applicability of the proposed method.

This paper investigates the problem of robust Hinfin state-feedback control for a class of discrete-time singular T-S fuzzy systems with norm-bounded parameter uncertainties. By taking into account the relationships between the slow and fast subsystems of a discrete-time singular T-S fuzzy system, a bounded real lemma is firstly derived, which is shown to be sufficient and necessary. Based on this, an explicit expression for the desired controller is given in terms of a set of strict linear matrix inequalities (LMIs), which involve no system decomposition.

A special guaranteed cost control problem is studied for a class of uncertain time-delay singular systems. Firstly, the system is transformed to an auxiliary system equipped with disturbance input, by regarding the parametric uncertainties as disturbance input. Then, sufficient conditions are presented, which not only make the closed-loop system regular, impulse free and asymptotically stable for all admissible uncertainties, but also guarantee an adequate level of performance. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired state-feedback control law and the upper cost bound are also given. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

A sliding mode control method is proposed for a class of multiply input and multiply output (MIMO) linear singular systems with unmatched uncertainties. Firstly, the singular system is transformed into the normal system by a derivative state feedback controller under the assumption that system is strong controllable. And then a terminal sliding mode manifold is designed and the control law is driven to reach the terminal sliding mode surface in finite time and converge to the neighborhood of equilibrium point in finite time once they are on the sliding mode manifold. The neighborhood of equilibrium is related with the range of unmatched uncertainties and parameters of terminal sliding mode. Finally, simulation example validates the design method.

Hybrid seven bar actuator is a typical planar parallel robot. It remains with position control following system. Position control accuracy of system determines the profile accuracy of hybrid actuator. According to the characteristics of the hybrid seven bar actuator, incorporating the grey prediction, repetitive control and the conventional PID control, a design method of the Grey prediction Repetitive PID control algorithm (GRPID) is presented for the first time. The hybrid control algorithm can estimate unsure parameters and disturbance of system using grey prediction, and compensate control in terms of the prediction results, and this may improve control quality and robustness of repetitive control for controlling periodic motion. The simulation results show that this algorithm has better performances than that of the conventional repetitive control system. It indicates the control method has better application effect for hybrid actuator taking on a characteristic of periodic motion.

A variable structure control method is proposed for a class of time-delay systems with mismatched norm-bounded uncertainties. We relax the matching assumption of traditional VSC design method, and the uncertain system under consideration may have mismatched parameter uncertainties in the state matrices as well as in the input matrix. In terms of linear matrix inequalities (LMIs), we give a delay-independent sufficient condition for the existence of sliding mode surface, on which sliding mode dynamics is asymptotically stable. A variable structure control law is also designed to guarantee system trajectories reach the sliding mode surface. Finally we give an example to show the effectiveness of our method.

A global nonsingular terminal sliding mode controller is proposed for a class of second order time delay systems with distributed in state and control variables. By properly designing a state transformation and a predictor, the given system can be transformed into a time delay free one, based on which we construct a new terminal sliding mode surface. Under the proposed terminal sliding mode controller, the system states can be driven to reach the new terminal sliding mode manifold and stay on it forever, resulting in the convergence to equilibrium in a finite time. The global stability of the closed loop system is guaranteed and the singularity problem associated with conventional terminal sliding mode is avoided.

A hybrid five bar actuator is a configuration that combines the motions of two characteristically different electric motors by means of a five bar mechanism to produce programmable output. Hybrid five bar actuator is the most representative one of hybrid actuator. In this paper, the method of kinematics and dynamics analysis for a hybrid five-bar actuator based on power bond graph theory is introduced. The bond graph model is provided. According to bond graph theory and model, dynamics equations can be derived. By means of the method, it is compact and convenient for solving the main driving power, the assist driving power of a hybrid five-bar actuator. The formula of dynamic equations derived here is a regularized one, and this procedure is very suitable for automatic derivation on a computer, obviously enhancing efficiency and reliability of dynamics analysis for hybrid five bar actuator. From this, a numerical example of kinematics and dynamics analysis for a hybrid five-bar actuator is given, and illustrates its validity.