In this paper, problems concerning robust impulse elimination for descriptor systems are considered. First, the concept of impulse margin is studied and based on which an upper bound is provided for the size of unstructured perturbations such that the descriptor system is guaranteed to be impulse-free. It is established that an arbitrarily large impulse margin may be specified provided that the descriptor system is both controllable and observable at infinity in the sense of Rosenbrock. This gives a new interpretation on controllability (observability) at infinity for descriptor systems as a counterpart of the arbitrary finite pole assignment of R-controllable descriptor systems. Then an output-feedback controller is synthesized to eliminate the impulses. It is also shown that a stabilizing state feedback controller can be designed after the impulses are eliminated with a specified perturbation margin against impulsive behaviour. Numerical optimization procedures are provided for maximizing or achieving a certain impulse margin of a descriptor system. Finally, a numerical example is given to illustrate the methodology presented in the paper.

While many algebraic properties of Lyapunov equation and LTI system are well known, few geometric properties, which may be used to analyze control system properties are studied. In this paper, some new necessary and sufficient conditions based on geometry are derived for properties of the Lyapunov equation and LTI system.

In this paper, a new type generalized Lyapunov equation for discrete singular systems is proposed. Then it is applied to study problems such as pole clustering, controllability and observability for discrete singular systems. First, some necessary and su6cient conditions for pole clustering are derived via the solution of this new type Lyapunov equation. Further, the relationship between the solution of the Lyapunov equation and structure properties of discrete singular systems will be investigated based on these results. Finally, a type of generalized Riccati equation is proposed and its solution is used to design state feedback law for discrete singular systems such that all the 8nite poles of the closed-loop systems are clustered into a speci8ed disk.

The problems of relaxed quadratic stability conditions, fuzzy observer designs and H∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two suffcient LMI conditions, which guarantee the existence of the H∞ controllers basedon fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers andthe H∞ controller designs based on new observers for the T-S fuzzy systems are very practical and effcient.