This paper addresses the L-gain filtering problem for continuous-time linear systems with time-varying structured uncertainties and non-zero initial conditions. We propose a full order linear filter that renders the L-gain from disturbance to filtering error within a prescribed level by solving a linear matrix inequality (LMI) feasibility problem. The filter gain is specified by the solution to a set of LMI's. A numerical example is given to illustrate the proposed method.

The robust induced l-norm control problem is considered for uncertain discrete-time systems. We propose a state feedback and an output feedback controller that quadratically stabilize the systems and satisfy a given constraint on the induced l-norm. Both controllers are constructed by solving a set of scalar-dependent linear matrix inequalities (LMI's), and the gain matrices are characterized by the solution to the LMI's.

The robust finite settling time stabilization problem is considered for a multivariable discrete time plant with structured uncertainties. Finite settling time (FST) stability of a feedback system is a notion introduced recently for discrete time systems as a generalization of the dead-beat response. The uncertain plant treated in this paper is described by (E0+ΣKi=1qiEi)x(t+1)(A0+ΣKi=1qiAi)x(t)+(B0+ΣKi=1qiBi)u(t), and y(t)=(C0+ΣKi=1qiCi)x(t) where Ei, Ai, Bi and Ci (0iK) are prescribed real matrices and qi (1iK) are uncertain parameters restricted to prescribed intervals [qi, i]. It is shown in this paper that a controller robustly FST stabilizes such an uncertain plant, if, the uncertain plant satisfies some conditions, and the controller simultaneously FST stabilizes a finite set of plants. The result leads to a testable necessary and sufficient condition of the existence of a solution to the robust FST stabilization problem, and a systematic method of designing a robust FST stable feedback system, in the case where the plant contains only one uncertain parameter.