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SUMMARYThis paper proposes a convex approach to regional stability and L 2 -gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input-to-output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential-algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the L 2 -gain of the input-to-output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full-order) output feedback controller with a guaranteed bound on the L 2 -gain. Numerical examples are used to illustrate the proposed approach.

This paper focuses on the problem of static anti-windup design for a class of multivariable nonlinear systems subject to actuator saturation. The considered class regards all systems that are rational on the states or that can be conveniently represented by a rational system with algebraic constraints considering some variable changes. More precisely, a method is proposed to compute a static anti-windup gain which ensures regional stability for the closed-loop system assuming that a dynamic output feedback controller is previously designed to stabilize the nonlinear system. The results are based on a differential algebraic representation of rational systems. The control saturation effects are taken into account by the application of a generalized sector bound condition. From these elements, LMI-based conditions are devised to compute an anti-windup gain with the aim of enlarging the closed-loop region of attraction. Several numerical examples are provided to illustrate the application of the proposed method.On the other hand, a key problem to characterize the stability of nonlinear systems is the determination of a nonconservative estimate of the system region of attraction. In general, the estimates are obtained from Lyapunov level sets (see, for instance, the references [17][18][19][20][21]). In this context, considering an NDI-based controller, the synthesis of a dynamic anti-windup compensator aiming at the enlargement of an estimate of the region of attraction of the closed-loop system in the subspace of the plant variables has been proposed in [22] for the class of quadratic systems. The considered architecture in this case, as in [12], can be seen as a generalization of the coprime-factorization approach (or the model recovery anti-windup) used in linear anti-windup [2,23]. This same problem has been tackled in [24] but considering rational systems and static anti-windup compensation. In particular, the multivariable case is not addressed, and the method is based on a nonconvex condition, although the problem solution is obtained from LMI relaxations. These drawbacks have been in part overcome in [25], where convex stabilizing conditions are proposed. However, it should be pointed out that in [24] and [25], only systems and controllers with linear outputs can be considered. It turns out that these approaches cannot be applied in the case of NDI controllers, for instance.In light of the aforementioned scenario, this paper aims at devising a numerical and tractable technique to design static anti-windup compensators for a class of nonlinear systems subject to actuator saturation. The class of systems considered in this paper covers all systems modeled by rational differential equations. The motivation to investigate rational systems is their use to model several phenomena in real life applications, in particular in systems biology, engineering, physics, and economics, and also in nonlinear system identification and realization theory [26,27], which has given rise to a large number of works on the stability a...