Stability Analysis and Stabilization of Systems Presenting Nested Saturations

Abstract

Abstract-This note addresses the problems of stability analysis and stabilization of systems presenting nested saturations. Depending on the open-loop stability assumption, the global stability analysis and stabilization problems are considered. In the (local) analysis problem, the objective is the determination of estimates of the basin of attraction of the system. Considering the stabilization problem, the goal is to design a set of gains in order to enlarge the basin of attraction of the closed-loop system. Based on the modelling of the system presenting nested saturations as a linear system with dead-zone nested nonlinearities and the use of a generalized sector condition, linear matrix inequality (LMI) stability conditions are formulated. From these conditions, convex optimization strategies are proposed to solve both problems.

Stability analysis and stabilization for singular linear systems subject to actuator saturation

“…The nonlinearity defined by (4) with = satisfies the following lemma which is directly derived from Lemma 1 in [12] or Lemma 2 in [13].…”

“…Compared with the above mentioned method, this LDI approach leads to less conservative conditions since it takes into account the specific properties of the saturation function rather than treats it as a locally sector bounded nonlinearity. More recently, the problems of stability analysis and stabilization of systems presenting nested saturations is addressed in [12]. By modeling the closed-loop system as a linear system with deadzone nested nonlinearities and the use of a generalized sector This condition (GVC), LMI based conditions are formulated.…”

“…Nonlinear feedback design method is given. It has been shown in [12], [13] that the numerical complexity associated to the GVC based methods increases slower than that associated the LDI based approachs. However, the conservativeness of the GVC based methods is not compared with that of the LDI based approachs.…”

Mean square synchronization of neural networks with Lévy noise via sampled-data and actuator saturating controller

“…[26][27][28][29][30], and the references therein). But in neural networks, due to the limited of the neuron's membrane potential, the actuator cannot acts an unlimited amplitude control signal.…”

Robust output feedback control of uncertain time-delay systems with actuator saturation and disturbances

“…The anti-windup compensator is used to weaken the negative effect of actuator saturation. For several decades, the control problem for the systems subject to actuator saturation has been extensively investigated in the literature (see, e.g., [1][2][3][4][5][6][7][8][9]). On the other hand, time-delay systems, which can be used to model abundant phenomena of practice, have been an active research area due to its theoretical significance and practical importance [10][11][12][13][14][15][16].…”