An LMI formulation for output feedback stabilization in multiple model approach

Abstract

This paper studies the design of a static output feedback controller for nonlinear systems described by multiple model approach. Motivated by quadratic stabilization result developed for parallel distributed compensation (PDC) controller, an Output PDC (OPDC) controller that corresponds to a nonlinear static output feedback control law is proposed. Both stabilization and pole placement are addressed, firstly by a cone complementarity formulation of the problem and secondly by transformation to linear matrix inequality (LMI) problem. An example is given to illustrate the results.

Introduction to Takagi–Sugeno Fuzzy Systems

“…A number of studies also provide nonquadratic Lyapunov functions of the form [25] and Chadli et al [26] have recently presented additional stability conditions using the following nonquadratic Lyapunov functions.…”

“…However, in the case where output matrix C is full rank line, a convex formulation with algebraic constraints(1.81) and (1.82) is proposed in [26]. Theorem 1.12 [21,26] IF there exist symmetric matrices Q ii and X >, and matrices Q ij with Q ji = Q T ij for i = j, and matrices N i satisfying: …”

Stabilization of Saturated Switching Systems

“…□ To achieve a domain of attraction as large as possible, we can solve similar optimization problem as for state feedback control. Another way to deal with the problem by relaxing the more constraining relations (45) of Theorem 2.6, especially in MIMO case, is presented by the following result which uses the same idea as in (El Ghaoui et al, 1997) and (Chadli et al, 2002).…”

Fault Tolerant Control Design For Polytopic Lpv Systems

“…Chadli et al (2002) developed an output feedback through LMIs in a multi-model context but only in a faultfree case. In (Rodrigues et al, 2005b), a solution was proposed in the same multi-model context with the aim to design a static state feedback which takes into account multiple actuator failures.…”