The purpose of this paper is to give a necessary and sufficient condition under which for a given plant of descriptor system model there exists a normal, internally stabilizing controller of order no greater than rankE that satisfies a closed-loop H , norm bound. The approach used in this paper is based on a generalized version of Bounded Real Lemma, thus the proofs are simple.

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This paper considers the synthesis of stabilizing controllers for nonlinear control-affine systems under multiple state constraints. A new control Lyapunov-barrier function approach is introduced for solving the considered problem. Assuming a classical control Lyapunov function, two possible methods for constructing new control Lyapunov-barrier functions are discussed. Sufficient conditions for the existence of new control Lyapunov-barrier functions are derived. With modifying the Sontag's formula, an explicit stateconstrained stabilizing feedback law is presented. Finally, two numerical examples are provided to illustrate the obtained theoretical results.

In this paper, su cient conditions for the existence of a solution to the non-linear H 1 ® ltering problem are presented. The conditions are expressed in terms of the solution to a Hamilton± Jacobi inequality involving only n ‡ 1 (for timevarying case) or n (for time-invariant case) independent variables. Both a ne and general non-linear systems are examined. In the time-invariant a ne non-linear case, one kind of positive radial solution to the Hamilton± Jacobi inequality is presented, and an explicit estimation of the achievable disturbance attenuation level is given. Illustrative examples are also included.

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