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

Abstract

This work deals with reduced-order Luenbergerlike observer design and control for switched affine systems. Formulation of state-dependent and dynamic outputdependent switching laws for those systems was already addressed, however, in a full-order treatment. The proposed procedure defines an estimator system only for the unmeasured part of the system state. Linear matrix inequalities for obtaining output gain matrices and for composing a reduced-order Luenberger observer-based switching law are proposed. Finally, the results are validated by design and simulation for DC-DC converters.

Multi‐rate sampled‐data control of switched affine systems

“…The control design problem for switched affine systems has been studied [19–21]. The objective of such problem is to design a switching strategy for all and determine the set of all equilibrium points , namely as .…”

Robust sampling‐based switching design for piecewise affine systems with application to DC–DC converters

“…and γ > 0, β > 0 are given scalar tuning parameters. Combining (19) and (20), one has e T (t)Σ i (t)e(t) + e T (t)…”

“…In addition to the methods described above, LMIs [17,18] and convex combination techniques [19] are widely used for switching rule design. In recent years, affine systems have received much research attention [20]. Obviously, the Lyapunov function method can be used to study the asymptotic stability of piecewise affine systems and its switching rule design.…”