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This paper deals with integral control of a class of switched affine systems characterised by time-varying differential equations that, along with the discontinuities caused by the switching, also depend periodically on an exogenous parameter, which is an affine function of time. The goal is to design a state-dependent switching function with integral action that ensures global asymptotic tracking of a trajectory of interest. The integral action is responsible for providing robustness to the system against uncertainties and load variations, whenever the discrepancy between the model and the real system is sufficiently bounded. Due to the integrator, all the convex combinations of the dynamic matrices are non-Hurwitz. In this case, the main difficulty is to guarantee that the time derivative of the Lyapunov function is strictly negative definite, which is done by means of LMIs and conditions on the affine terms. To the best of our knowledge, this is the first Lyapunov-based switching rule with integral action able to ensure global asymptotic tracking of a pre-specified profile. When applied to AC circuits the advantage is to design the switching rule based on the original system, without resorting to averaged models. The theory is illustrated by the control of a three-phase AC-DC converter. [ABSTRACT FROM AUTHOR]

This paper deals with the output feedback [H.sub.[infinity]] control design problem for continuous-time switched linear systems. More specifically, the main goal is to design a switching rule together with a dynamic full order linear controller to satisfy a prespecified [H.sub.[infinity]] level defined by the [L.sub.2] gain from the input to the output signal. Initially, the state feedback version of this problem is solved in order to put in evidence the main difficulties we have to face toward the solution of the output feedback control design problem. The results reported in this paper are based on the so called Lyapunov--Metzler inequalities, which express a sufficient condition for switched linear systems global stability. The solution of the previously mentioned output feedback control design problem through a linear matrix inequality based method is the main contribution of the present paper. An academic example borrowed from literature is used for illustration. [DOI: 10.1115/1.4001711]

This paper treats the control design of an output-dependent switching function for discrete-time switched linear systems, without considering the synthesis of any additional dynamic structure. The conditions are based on a convex, but time-varying, Lyapunov function and are expressed in terms of Linear Matrix Inequalities (LMIs). The state feedback switching function design can be obtained as a particular case and is simpler to handle from theoretical and numerical viewpoints compared to other methods available in the literature, as for instance, those based on Lyapunov–Metzler inequalities. The novelty of the proposed control methodology is the adoption of a time-varying Lyapunov function, which together with the presence of a key matrix, allow us to treat the static output feedback control design, taking into account a guaranteed H 2 performance cost. Academic examples are used for comparison and illustration. The proposed control technique is experimentally validated in an active suspension system representing a quarter-vehicle. [ABSTRACT FROM AUTHOR]