and Applied Analysis 3 2. Main Results Firstly, we give some notation. The space of all infinitely differentiable functions φ t, x with compact support in 0, ∞ ×R is denoted byC∞ 0 . L L R 1 ≤ p < ∞ is the space of all measurable functions h such that ‖h‖pLp ∫ R |h t, x |pdx < ∞. We define L∞ L∞ R with the standard norm ‖h‖L∞ infm e 0supx∈R\e|h t, x |. For any real number s, H H R denotes the S...

Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...

A b g r a a A simultaneous H2/H® control problem is considered. This problem seeks to minimize the H 2 norm of a closed-loop transfer matrix while simultaneously satisfying a prescribed H~ norm bound on some other closed-loop transfer matrix by utilizing dynamic state feedback controllers. Such a problem was formulated earlier by Rotea and Khargonekar (Automatica, 27, 307-316, 1991) who conside...

In this paper we consider the robust performance problem in H 1 with scalar perturbations. We illustrate how the worst case H 1 performance can be regarded as an H 1 norm of a function of several complex variables. Alternatively, a method is presented for computing the worst case performance by computing the H 1 norm of a single system. This system is constructed from the original nominal syste...

A linear matrix inequality approach to synthesizing low-order suboptimal mixed l /H N controllers ଝ Abstract Mixed objective control problems have attracted much attention lately since they allow for capturing di!erent performance speci"cations. However, optimal multiobjective controllers may exhibit some undesirable properties such as arbitrarily high order. This paper addresses the problem of...

Abstract : In this paper we consider the mixed H /H -control problem for the class of discrete-time 2 _ linear systems with parameters subject to Markovian jumps (MJLS). It is assumed that both the state variable and the jump variable are available to the controller. The transition probability matrix may not be exactly known, but belongs to an appropriate convex set. For this controlled discret...

Let Ω a bounded regular1 domain of R and let us denote respectively by | · | and (·, ·) the natural norm and inner product of the space H = L2(Ω). Let V →֒ H be a real Hilbert space that is continuously and densely embedded into H. Denote by ‖ · ‖ and < ·, · >V respectively the norm and the inner product of V and by L ∈ L(V, V ) the unique linear continuous operator from V to V , the dual of V ,...

This paper is aimed at extending the H∞ Bounded Real Lemma to stochastic systems under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in entropy theoretic terms using the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is a stochastic counterpart of the ...