Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

The existence of the time-delay phenomena in a dynamic system may cause instability or bad system performances in openand closed-loop systems (Kolmanoskii & Myshkis, 1992). The stability analysis and robust control problems for time-delay systems have been considered in the past years (Lien & Chen, 2003; Moon et al., 2001; Nian & Feng, 2003; Park, 2003; Sun, 2002; Xu et al., 2003). However, in practical applications, such as system supervision, gas-fired furnace system and fault diagnosis, the system states are not usually measurable or have no practical senses. On the other hand, the system model always contains some uncertain elements; these uncertainties may be due to additive unknown noise, environmental influence, nonlinearities such as hysteresis or friction, poor plant knowledge, reducedorder models and uncertain or slowly varying parameters. Hence, the observer for the uncertain system will be useful and applied to reconstruct the states of a dynamic system. In this situation, the robust observer-based control will be more suitable than the state feedback control for the system (Sun, 2002). Hence, an efficient method to design the robust observer-based control for uncertain time-delay system is very important. In the recent years, the system performance requirements are the other considering works for the control engineers and researchers. Thus, the guaranteed cost control will be the useful system representation of performance (Nian & Feng, 2003; Park, 2003; Xu et al., 2003). Depending on whether the stabilization criterion itself contains the size of delays, stabilization criteria of time-delay systems can be classified into two categories, namely delay-independent criteria (Park, 2003; Xu et al., 2003) and delay-dependent criteria (Nian & Feng, 2003; Sun, 2002). Generally speaking, the latter ones are less conservative than the former ones when the time-delay values are small. The time-delay systems can be mainly classified into two types, namely retarded systems (Moon et al., 2001; Nian & Feng, 2003) and neutral systems (Park, 2003; Sun, 2002; Xu et al., 2003). The systems whose dynamics only depend on the delay of state are called the retarded time-delay systems. The systems whose dynamics depend on the delays of state and state derivative are called the neutral time-delay systems. Neutral time-delay systems are encountered in modelling chemical reactors, dynamic process including steam