Stability analysis for a class of switched nonlinear systems

Stabilization and robust H∞ control for sector-bounded switched nonlinear systems

“…However, stability of a composed switched system cannot be concluded from the stability of subsystems (Liberzon, 2003). Stability under arbitrary switching for system (1) with A i = 0 using a common Lyapunov function of the form (6) but without the quadratic term is proposed by Aleksandrov et al (2011). However, extension of the results obtained by Aleksandrov et al (2011) to our more general model (1)-(3) and more important, to the robust stabilization problem is not possible.…”

“…Note that the functions f i are neither required to lie only in the 1st and the 3rd quadrant as in Gonzaga et al (2012), nor to have unbounded integrals as in Aleksandrov et al (2011) and Kazkurewicz and Bhaya (1999).…”

“…Thus, in the non-switched case, we cover more general cases of nonlinear functions compared e.g. to the Lure' type systems studied by Castelan, Tarbouriech, and Queinnec (2008), Gonzaga, Jungers, and Daafouz (2012) and to the nonlinear systems that admit diagonal-type Lyapunov functions investigated by Aleksandrov et al (2011) and Kazkurewicz and Bhaya (1999). Our paper contains 3 main contributions with respect to the state-of-the-art: (1) inclusion of sector bounds with arbitrary slopes for nonlinear functions (moreover, the nonlinear functions are no longer required to have an unbounded integral), (2) stability analysis for this class of switched systems under arbitrary switching using a less conservative approach based on multiple Lyapunov functions and the concept of average dwell time, (3) stabilization and robust disturbance attenuation of these systems using a bilevel convex optimization problem.…”

“…uncertainty in parameters, or specific applications that utilize switching between controllers in order to achieve a higher performance (Aleksandrov, Chen, Platonov, & Zhang, 2011;Geromel, Deaecto, & Daafouz, 2013;Hu, Ma, & Lin, 2008;Liberzon, 2003).…”

Output Feedback Control of Switched Nonlinear Systems: A Gain Scheduling Approach

“…For switched linear systems, finding the common Lyapunov function is relatively easy but for nonlinear systems it is difficult. A survey of switched nonlinear systems can be found in [2,14,20,29]. Due to the switched controller design problems for continuous and discrete time nonlinear systems, in this note we pursue the idea to use -instead of a model of a nonlinear switched plant -a model of the switched gain scheduled plant and to design a switched gain scheduled controller guaranteeing closed loop stability and an optimal value of a given quadratic novel cost function for all operating points of the switched nonlinear system.…”