Observer-Based Control Design for Switched Affine Systems and Applications to DC–DC Converters

An LMI Approach to Full- and Reduced-Order Switched Luenberger Observers for Switched Affine Systems

“…Those theorems inserted matrix blocks for enhancing the state estimation by guaranteeing an upper bound for the error energy as in (16). As previous results given by Yoshimura et al (2013), Deaecto et al (2010) and Mainardi Júnior et al 2012, Theorem 1 has an immediate application, the DC-DC converters. Although Theorem 2 presents no immediate application, that result is important as it could also be applied to DC-DC converters and completes the theory on full-order SASs state estimation.…”

“…Both in (6) and 7, L ∈ R n×m is the output gain matrix. Yoshimura et al (2013) noted that, by modifying Luenberger's idea, an observer for SASs could be devised. The proposed estimator system waṡ…”

“…However, due to σ , J is not differentiable and, therefore, very difficult to minimize (Deaecto et al 2010). However, an upper bound for the functional can be established, using ideas from Deaecto et al (2010) and Yoshimura et al (2013). Firstly, define the error vector…”

“…LMIs are widely used in control theory (Boyd et al 1994) and an LMI-proposal of a dynamic output-dependent switching law for SASs was addressed by Yoshimura et al (2013): using the sensed output and imposing the same switching law to the plant and to the estimator, the estimated state could be used to substitute the real state.…”

Robust Control of Switched Linear Systems with Output Switching Strategy

“…In recent decades, the scientific community has shown a growing interest in the study of the stability of switched linear systems (Geromel and Colaneri 2006;Zhai et al 2003). This interest is mainly due to the fact that they usually allow a better overall performance, namely their applications in practical systems such as: mechanical control systems, process control, power systems, aircraft control, automotive industry, power electronics (Yoshimura et al 2013;Scharlau et al 2014;Mainardi Júnior et al 2012a;Cardim et al 2009;Deaecto et al 2010). In general, the theory of switched linear systems can be divided into two groups, where the first one occurs when the switching strategy σ (t) is independent of the system state variables and the second one occurs when σ (t) is a control variable dependent on the state variables of the system (Geromel and Colaneri 2006).…”