Global Regulation of a Class of Uncertain Nonlinear Systems by Switching Adaptive Controller

Dynamic gain control with a matrix inequality approach to uncertain systems with triangular and non-triangular nonlinearities

“…, the existing controllers in Chen and Huang (2009), Lim (2005, 2010), Ding et al (2010Ding et al ( , 2012, Koo et al (2010Koo et al ( , 2012, Krishnamurthy and Khorrami (2007), Krstic (2002), Lei and Lin (2006), Polendo and Qian (2007), Praly (2003), Qian and Lin (2001), Xudong (2003Xudong ( , 2005, and Ye and Unbehauen (2004) are not applied to the transformed system (65). In this case, δ i (t, z, u) = 0, for i = 1, 3, 4, and δ 2 (t, z, u) = θ 3 x 3 + d 5 …”

“…The triangular structure can be divided into two types: lower triangular type and upper triangular type. The lower triangular condition is the so-called 'triangular condition' and the upper triangular condition is the so-called 'feedforward condition' in existing results (Chen & Huang, 2009;Choi & Lim, 2005Ding, Qian, & Li, 2010;Ding, Li, & Zheng, 2012;Koo, Choi, & Lim, 2010Krishnamurthy & Khorrami, 2007;Krstic, 2002;Lei & Lin, 2006Polendo & Qian, 2007;Praly, 2003;Qian & Lin, 2001;Xudong, 2003Xudong, , 2005Ye & Unbehauen, 2004). Generally, the two types of triangular structures are described by (i) Lower triangular form:…”

“…Global regulation or stabilisation problems under the linear growth lower triangular condition (Choi & Lim, 2005;Koo et al, 2010;Lei & Lin, 2006) and the linear growth upper triangular condition (Chen & Huang, 2009;Choi & Lim, 2005;Koo et al, 2010;Krstic, 2002;Xudong, 2003Xudong, , 2005 have been solved, respectively. In extended results, several independent controllers are presented to solve the regulation or stabilisation problems of the nonlinear systems with a non-triangular structure as higher order nonlinearities (Koo et al, 2012;Krishnamurthy & Khorrami, 2007;Lei & Lin, 2007Polendo & Qian, 2007;Qian & Lin, 2001) and lower order nonlinearities (Ding et al, 2010(Ding et al, , 2012.…”

“…The lower triangular conditions in Lim (2005, 2010), Koo et al (2010), and Lei and Lin (2006) are included in Assumption 1.1, and the upper triangular condition in Chen and Huang (2009), Choi and Lim (2005), Koo et al (2010), Krstic (2002), Xudong (2003Xudong ( , 2005 and Ye and Unbehauen (2004) are included in Assumption 1.2. and φ T2 (x, u, γ (t)) = |x 1 | 2 . Then, Assumption 1.1-(A3) is satisfied by taking a T(1, 1) = 0, a T(1, 2) = 0, μ T1 = 1/5, ν T1 = 0, a T(2, 1) = 2, a T(2, 2) = 0, μ T2 = 0, and ν T2 = 0.…”

Observer based output feedback regulation of a class of feedforward nonlinear systems with uncertain input and state delays using adaptive gain

“…For example, some electrical circuit systems in [23] or chemical reactor systems in [24], and their variants can be transformed to the systems that fit the system (2) with Assumption 1.…”