Robust H∞ filter design for discrete-time switched systems with interval time-varying delay and linear fractional perturbations: LMI optimization approach

Keywords: H 1 filter design Discrete-time switched system Interval time-varying delay LMI optimization approach a b s t r a c t In this paper, the robust H 1 filter scheme for the discrete-time switched systems with interval time-varying delay and linear fractional perturbations is proposed. A convex optimization problem with some LMI constraints is formulated to design the stable switched filter which minimizes the H 1 norm bound for filtering error system. Some nonnegative inequalities and the free weighting matrix technique are used to provide the additional degree of freedom which improves the conservativeness of the proposed results. Finally, a numerical example is illustrated to show the use of the main results. Switched systems are often encountered in many practical systems including automated highway systems, automotive engine control systems, chemical process, constrained robotics, power systems and power electronics, robot manufacture, and stepper motors. A switched system consists of several subsystems and a discrete switching signal. Hence a switched system is a hybrid system. Switching among subsystems may produce many complicate nonlinear system behaviors, such as chaos and multiple limit cycles [1,2]. It is also well known that the existence of time delay in a system may cause instability or bad performance in closed loop control systems. Time-delay phenomena are usually confronted in many practical systems , such as AIDS epidemic, chemical engineering systems, hydraulic systems, inferred grinding model, neural network, nuclear reactor, population dynamic model, and rolling mill [3–5]. There are two interesting facts in switched system: the first one is that stability of a switched system can be achieved by choosing the switching signal even when each subsystem is unstable [6–9]. The another one is that the stable property for each subsystem cannot imply that the overall switched system is also stable under arbitrary switching signal [10,11]. Hence stability and stabilization problems for switched systems with time delay have been investigated in recent years [1,6–11]. Filtering problem is playing an important role in control applications and signal processing over past years, because it has been applied in practical engineering such as biomedical systems , manufacturing, process control, mechatronics [12]. The celebrated Kalman filter assumes that the system model and statistical information of noise are precisely known. However, these assumptions are actually questionable and usually not practical. Hence H 1 filtering technology was introduced in [13] and has been provided in diverse systems, such as fuzzy