Riccati equation

About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.

${\cal H}_\infty$ Control and Estimation Problems with Delayed Measurements: State-Space Solutions

Abstract: Most physical processes exhibit transport delay in the measured output, and it is well known that this can have disastrous effects on system stability and performance if it is not accounted for. In this paper, we give necessary and sufficient conditions for existence of estimators and controllers that achieve the desired ${\cal H}_\infty$ performance criterion when such a measurement delay is present. We also give the complete characterization of all controllers and estimators that achieve the desired performance criterion. The necessary and sufficient conditions are easy to check and are given in terms of the familiar pair of algebraic Riccati equations that appear in the nondelay versions of the corresponding ${\cal H}_\infty$ problems, along with an additional Riccati differential equation. Explicit state-space formulas for the controllers and estimators are also obtained. They have a linear periodic structure and are easily implementable. To obtain these results, we first obtain state-space results for a "modified" Nehari problem, which may be of independent interest (see Problem 5 in section 2).

Quadratic stabilization of uncertain discrete-time fuzzy dynamic systems

Abstract: New approaches to quadratic stabilization of uncertain discrete-time fuzzy dynamic systems are developed in this paper. This uncertain fuzzy dynamic model is used to represent a class of uncertain discrete-time complex nonlinear systems which include both linguistic information and system uncertainties. It is shown that the uncertain fuzzy dynamic system is stabilizable if a suitable Riccati equation or a set of Riccati equations have solutions. Constructive algorithms are also developed to obtain the stabilization feedback control laws. Finally, an example is given to illustrate the application of the proposed method.

Optimal pole shifting for continuous multivariable linear systems

Abstract: A method for shifting the real parts of the open-loop poles to any desired positions while preserving the imaginary parts is presented. The method is based on the mirror-image property which has been reported by Molinari. In other words, Molinari's results are extended and then a recursive approach is developed. In each step of this approach, it is required to solve a first-order or a second-order linear matrix Lyapunov equation for shifting one real pole or two complex conjugate poles respectively. The presented method yields a solution which is optimal with respect to a quadratic performance index. The attractive feature of this method is that it enables solutions to complex problems to be easily found without solving any non-linear algebraic Riccati equation.