Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find such that norm of closed-loop transfer function is (strictly) less than . It known controller exists if and only unique stabilizing solutions to two algebraic Riccati equations positive definite spectral radius their product /sup 2/. Under these conditions, parameterization problem as linear fractional transformation (LFT) on contractive,...

Abstract The problem of approximating a multivariable transfer function G(s) McMillan degree n, by Ĝ(s) k is considered. A complete characterization all approximations that minimize the Hankel-norm derived. solution involves rational functions + F(s) where has k, and anticavisal. to latter via results on balanced realizations, all-pass inertia matrices, in terms solutions Lyapunov equations. It then shown σ k+1(G(s)) (k+l)st Hankel singular value for one class optimal approximations. method...

A design procedure is introduced which incorporates loop shaping methods to obtain performance/robust stability tradeoffs, and a particular H/sub infinity / optimization problem guarantee closed-loop level of robust at all frequencies. Theoretical justification this technique given, the effect on behavior examined. The illustrated in controller for flexible space platform.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simple state-space formulas are presnted for a con- boler solving andard 74.-prObkem.The controllr has the same sateimension as plant, its computation involves wl two Ricati eq and it ha separation structure remiuscent of classical LQG (i.e., X2) theory.This paper is also intended to be tutoal value, so standard 74-solUtion developed in parallel.

The problem of robustly stabilizing a family linear systems is explicitly solved in the case where characterized by H/sub infinity / bounded perturbations to numerator and denominator normalized left coprime factorization nominal system. This can be reduced Nehari extension directly gives an optimal stability margin. All controllers satisfying suboptimal margin are characterized, explicit state-space formulas given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML"...

This short paper considers the identification of dynamical systems from input-output data. The problem parameter identifiability for such is approached by considering whether system outputs obtained with different values can be distinguished one another. results are stated formally defining notion "output distinguishability." Parameter then defined precisely in terms output distinguishability. Relationships have been developed other definitions as least square and transfer function. Several...

We consider the problem of what parametrizations linear dynamical systems are appropriate for identification (i.e., so that has a unique solution, and all particular class can be represented). Canonical forms controllable under similarity transformation considered it is shown their use in may cause numerical difficulties, an alternate approach proposed which avoids these difficulties. Then assumed system matrices parametrized by some unknown parameters from priori knowledge. The...

This paper considers the analysis and synthesis of control systems subject to two types disturbance signals: white signals with bounded power. The resulting problem involves minimizing a mixed /spl Hscr//sub 2/ infin// norm system. It is shown that controller shares separation property similar those pure or controllers. Necessary conditions sufficient are obtained for existence solution problem. Explicit state-space formulas also given optimal controller.< <ETX...

This paper introduces an induced-norm formulation of a mixed /spl Hscr//sub 2/ and infin// performance criterion. It is shown that different norms arise from assumptions on the input signals. While most can be expressed explicitly using either transfer functions or state-space realizations system, there are cases where explicit formulas very hard to obtain. In later cases, examples given show intrinsic nature difficulty problem. Mixed norm robust analysis under structured uncertainty also...

Model reduction methods are presented for systems represented by a linear fractional transformation on repeated scalar uncertainty structure. These involve complete generalization of balanced realizations, Gramians, and truncation model with guaranteed error bounds, based solutions to pair matrix inequalities which generalize Lyapunov equations. The resulting immediately apply simplification state order in the case uncertain but also may be interpreted as multidimensional systems.

All solutions to the four block general distance problem which arises in $H^\infty $ optimal control are characterized. The procedure is embed original an all-pass matrix constructed. It then shown that part of this acts as a generator all solutions. Special attention given characterization by invoking new descriptor transfer functions. As application, necessary and sufficient conditions found for existence controller. Following that, representation derived.

The class of linear infinite-dimensional systems with finite-dimensional inputs and outputs whose impulse response h satisfies $h \in L_1 \cap L_2 (0,\infty ;\mathbb{C}^{p \times m} )$ induces a nuclear Hankel operator is said to be type. For this it shown that balanced or output normal realisations always exist their truncations converge the original system in various topologies. Furthermore, explicit $L_\infty$ bounds on transfer function errors, $L_1$ $L_2$ Hilbert-Schmidt errors are...

The authors apply H/sub infinity /-designed controllers to a generic VSTOL (vertical and short takeoff landing) aircraft model GVAM. design study motivates the use of / techniques, addresses some implementation issues which arise for multivariable controllers. An approach gain scheduling on basis normalized comprime factor robust stabilization problem formulation used is developed. It utilizes observer structure unique this particular robustness optimization. A weighting selection procedure,...

A self-contained algebraic derivation of the necessary and sufficient conditions for a multiinput system with fixed zero structure to be structurally controllable is given. In addition, new recursive test determining structural controllability which utilizes only Boolean operations obtained.

Necessary and sufficient conditions for the existence of suboptimal solutions to standard model matching problem associated with $\mathcal{H}_\infty $ control, J control are derived using J-spectral factorization theory. The is shown be equivalent two coupled problems, second factor providing a parametrization all problem. factors then nonnegative definite, stabilizing indefinite algebraic Riccati equations, allowing state-space formula linear fractional representation controllers given. A...

Abstract State-space solutions to a discrete-time ℋ∞ problem are given. For given number γ>0we give characterization of all controllers such that the ℋ ∞ norm closed-loop transfer function is less than γ The approach taken based on solution two Riccati equations using stable deflating subspace symplectic pencil. This ensures no unnecessary assumptions 'A' matrix realization needed. While results direct analogues those in continuous time, state-space derivation considerably more difficult.