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.

A linear matrix inequality approach to peak‐to‐peak gain minimization

Abstract: In this paper we take a new approach to the problem of peak-to-peak gain minimization (the L1 or induced L∞ problem). This is done in an effort to circumvent the complexity problems of other approaches. Instead of minimizing the induced L∞ norm, we minimize the * -norm, the best upper bound on the induced L∞ norm obtainable by bounding the reachable set with inescapable ellipsoids. Controller and filter synthesis for * -norm minimization reduces to minimizing a continuous function of a single real variable. This function can be evaluated, in the most complicated case, by solving a Riccati equation followed by an LMI eigenvalue problem. We contend that synthesis is practical now, but a key computational question-is the function to be minimized convex?—remains open. The filters and controllers that result from this approach are at most the same order as the plant, as in the case of LQG and H∞ design.

Pole assignment in a specified disk

Abstract: The problem of assigning all poles of a closed-loop system in a specified disk by state feedback is considered for both continuous and discrete systems. A state feedback control law is determined by using a discrete Riccati equation. This kind of pole assignment problem is named D -pole assignment, and its relation to the optimal control problem and its robustness properties are discussed. The gain and phase margins for all closed-loop poles to stay inside the specified disk D are determined for the proposed control.

Filtering on sampled-data systems with parametric uncertainty

Abstract: The paper is concerned with the problem of robust H/sub /spl infin// filtering for a class of systems with parametric uncertainties and unknown time delays under sampled measurements. The parameter uncertainties considered are real time-varying and norm-bounded, appearing in the state equation. An approach has been proposed for the designing of H/sub /spl infin// filters, using sampled measurements, which would guarantee a prescribed H/sub /spl infin// performance in the continuous-time context, irrespective of the parameter uncertainties and unknown time delays. Both cases of finite and infinite horizon filtering are studied. It has been shown that the above robust H/sub /spl infin//-filtering problem can be solved in terms of differential Riccati inequalities with finite discrete jumps.