Control of systems with actuator saturation non-linearities: An LMI approach

Stability and performance analysis of saturated systems via partitioning of the virtual input space

“…The introduction of the saturation/deadzone function in the Lure-Postnikov type Lyapunov function (Gomes da Silva et al, 2002;Kapila et al, 2001) and the piecewise quadratic Lyapunov function (Dai et al, 2009) provides an extra degree of freedom in the resulting stability and performance conditions. However, the information inherent in the saturation/deadzone function has not been fully exploited and entails further exploration.…”

“…A saturation-dependent Lyapunov function was proposed in Cao and Lin (2003) that takes into account the severity of the actuator saturation. An integral of the saturation/deadzone function was added to a quadratic Lyapunov function to form a Lure-Postnikov type Lyapunov function (Gomes da Silva, Tarbouriech, & Reginatto, 2002;Kapila, Sparks, & Pan, 2001). This Lure-Postnikov type Lyapunov function was generalized in Dai et al (2009) to a piecewise quadratic Lyapunov function of an augmented state vector that contains the system states and the saturation/deadzone function.…”

A Generalized Piecewise Quadratic Lyapunov Function Approach to Estimating the Domain of Attraction of a Saturated System∗∗This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61221003 and 61273105.

“…Recently, a class of quadratic functions of the augmented state vector that contains the system state and saturation/deadzone function of the input have been employed to estimate the domain of attraction of saturated linear systems [3,4,10,12]. An integral of the saturation/deadzone function of the state is added to a quadratic Lyapunov function to form a Lure-Postnikov type Lyapunov function [4,10].…”

Adaptive Control with Guaranteed Contraction Rate for Systems with Actuator Saturation

“…Though a constant Lyapunov function can greatly facilitate the analysis and synthesis, the results obtained within time-invariant framework can be somewhat conservative. For this reason, some recent efforts have been made towards the construction of nonquadratic Lyapunov functions that may lead to LMIs or bilinear matrix inequalities (BMIs), see, e.g., Kapila et al [10] for a Lure-Postnikov type Lyapunov function, and Mulder and Kothare [12] and Johansson and Rantzer [9] for the type of piecewise quadratic Lyapunov functions. Some recent works provided novel ideas in constructing Lyapunov functions for saturated systems, see, e.g., Hu et al [8] for a combined quadratic function method consisting of both quadratic and nonquadratic Lyapunov functions, and Lin and Saberi [11] for a parametric Lyapunov equation approach.…”