Improved computation of ellipsoidal invariant sets for saturated control systems

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

“…for saturated systems. Moreover, the authors of Alamo et al (2005) presented an improved treatment with more auxiliary matrices than the representation in Hu and Lin (2001). A generalized sector condition that is able to provide a tighter bound of the saturation function than the linear sector was proposed in Hu, Huang, and Lin (2004).…”

“…The estimations of the domain of attraction (Alamo, Cepeda, & Limon, 2005;Cao & Lin, 2003;Dai, Hu, Teel, & Zaccarian, 2009;Gomes da Silva & Tarbouriech, 2005;Hu & Lin, 2001Hu, Teel, & Zaccarian, 2006;Li & Lin, 2013) and the nonlinear L 2 gain (Crawshaw & Vinnicombe, 2000;Hu et al, 2006;Hu, Teel, & Zaccarian, 2008;Wu & Soto, 2004;Zaccarian & Teel, 2004) play a very important role in analysis of linear systems under saturated feedback. This is especially so for systems that cannot be globally or semi-globally stabilized.…”

Tracking of REMUS autonomous underwater vehicles with actuator saturations

“…Contrary to previous LMI-based results (Feng & Allen, 2004;Innocenti & Campa, 1999;Roche et al, 2010;Silvestre & Pascoal, 2004), the approach adopted here is based on not linear but nonlinear kinematics and dynamics of the given AUV by taking the technique of sector nonlinearity (Tanaka & Wang, 2001), which enables an analysis based on its equivalent polytopic linear parameter varying (LPV) model at least locally by virtue of no linearization. Moreover, motivated by Alamo, Cepeda, and Limon (2005), the nonlinearity of the actuator saturation is incorporated in the design. However, by utilizing S-procedure (Yakubovich, 1971) instead of an inequality property of absolute value (see, Property 2 in Alamo et al (2005)), the proposed technique can be introduced in a less restrictive straightforward manner.…”

“…Moreover, motivated by Alamo, Cepeda, and Limon (2005), the nonlinearity of the actuator saturation is incorporated in the design. However, by utilizing S-procedure (Yakubovich, 1971) instead of an inequality property of absolute value (see, Property 2 in Alamo et al (2005)), the proposed technique can be introduced in a less restrictive straightforward manner. It is shown that under the feedback linearization, two available control inputs, the rudder angle and the propeller thrust can be designed separately.…”

Ellipsoidal approximations to attraction domains of linear systems with bounded control

“…Since recently, much attention has been paid to characterization of attraction domains for systems driven by saturated linear control, in particular, [4]- [11], and especially, [6]- [10].…”