Positive polynomials and robust stabilization with fixed-order controllers

Positive polynomials and robust stabilization with fixed-order controllers

Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coefficients of a polynomial. An application to the design of fixed-order controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed, based on LMI optimization. The key ingredient in the design procedure resides in the choice of a...

Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant FO-LTI systems. To determine the control parameters, one needs only a little knowledg...

A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-order Controllers

Stabilization by static output feedback (SOF) is a long-standing open problem in control: given an n by n matrix A and rectangular matrices B and C, find a p by q matrix K such that A + BKC is stable. Low-order controller design is a practically important problem that can be cast in the same framework, with (p+k)(q+k) design parameters instead of pq, where k is the order of the controller, and ...

Stabilization with J-dissipative Controllers

Let J = diag(1,−1), and let B be a controllable behavior. Let Bdes be a stable, autonomous subspace of B representing the desired behavior after feedback interconnection with some controller C. In this paper we address the following questions: does there exist a J-dissipative controller C such that C∩B = Bdes? How many unstable poles does the transfer function associated with the controllable p...

Robust Stabilization of Robotic Manipulators by PID Controllers