Static output feedback simultaneous stabilization: ILMI approach

Abstract

S tatic output feedback simultaneous stabilization: ILMI approach* YONG-YAN CAO² and YOU-XIAN SUN²In this note, the static output feedback simultaneous stabilization problem is addressed using a matrix inequality approach. A necessary and su cient condition for simultaneous stabilizability of r proper MIMO plants via static output feedback is obtained. It is proven that the existence of a stabilizing feedback gain which simultaneously stabilizes this set of plants is equivalent to that of the solution of a set of coupled quadratic matrix inequalities. An iterative LMI (ILMI) algorithm based on the linear matrix inequality technique is proposed to obtain the feedback gain. Illustrated examples show its e ectiveness.

Static output feedback based fault accommodation design for continuous-time dynamic systems

“…However, because of the nonconvex formulation of the SOF implementation, its necessary and sufficient condition is not numerically tractable. Coping with this difficulty generally requires using iterative LMIs (Cao and Sun 1998;Huang and Nguang 2006), equality constraints (Crusius and Trofino 1999;Chang, Park, Joo, and Chen 2003), diagonal Lyapunov matrices (Lo and Lin 2003) and so on. Obviously, these limitations and constraints are strict and increase the implementation complexity.…”

Robustness of proper dynamic output feedback for discrete-time singularly perturbed systems

“…In fact, there are a lot of existing works addressing this problem, and various methods have been proposed, e.g., Riccati equation approach, rankconstrained condition, approach based on structural properties, bilinear matrix inequality (BMI) approaches, min-max optimization techniques, and linear matrix inequality approaches [28,29]. Among them, the LMI approaches are much more efficient in dealing with synthesis problems [30][31][32], thus many results have also been obtained. In addition, the survey on the development of static output feedback can be found in [33].…”

A nonlinear minimization approach to multiobjective and structured controls for discrete‐time systems

“…In References [1,9], common Lyapunov matrices were used to obtain multiobjective controls. In References [2,10] and Reference [5], iterative LMI (ILMI) approaches were proposed for multiobjective controls and decentralized output feedback control, respectively. As a global search method, a genetic algorithm was proposed for mixed H 2 =H 1 PID control in Reference [7].…”

“…The multiobjective control problem is defined as the problem of finding a controller such that multiobjective specifications are met, for example, mixed H 2 =H 1 control and simultaneous stabilization [1][2][3]. The structured control problem is defined as the problem of finding a controller such that the structure of the controller is specified a priori, such as in decentralized control and fixed-order control [4][5][6].…”