Matrix spectral factorization is traditionally described as finding spectral factors having a fixed analytic pole configuration. The classification of spectral factors then involves studying the solutions of a certain algebraic Riccati equation which parametrizes their zero structure. The pole structure of the spectral factors can be also parametrized in terms of solutions of another Riccati eq...

The paper presents a new approach to the robust H ∞ control of an uncertain system via an output feedback controller which is both stable and positive real. The uncertain systems under consideration contain structured uncertainty described by integral quadratic constraints. The controller is designed to achieve absolute stabilization with a specified level of disturbance attenuation. The main r...

This paper provides a numerical approximation theory of algebraic Riccati operator equations with unbounded coefficient operators A and B , such as arise in the study of optimal quadratic cost problems over the time interval [0, oo] for the abstract dynamics y = Ay + Bu . Here, A is the generator of a strongly continuous analytic semigroup, and B is an unbounded operator with any degree of unbo...

First-order necessary conditions for quadratically optimal, steady-state, fixed-order dynamic compensation of a linear, time-invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form. In contrast to the pair of matrix Riccati equations for the full-order LQG case, the optimal steady-state fixed-order dynamic compensator is characterized...

Systematic strategies for optimal actuator and sensor locations require £nding extrema of control performance measures. When the control is designed for a distributed parameter system, these performance measures frequently involve the kernel of the Riccati operator or that of the feedback operator. For example, measuring the optimal linear quadratic regulator (LQR) cost over a range of initial ...

In this note we present equations that uniquely determine the maximumpossible imaginaryvalue of the closed loop eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen, provided a real symmetric solution of the algebraic Riccati equation exists. In addition, the corresponding state weight matrix and the solution to the algebraic Riccati equation are derived fo...