SummaryIn this report the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a polyhedral Lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms. The technique can be used to prove the stability of switched linear systems, classes of linear timevarying systems and Linear Differential Inclusions.We also present preliminary results on two other related problems; namely, the existence of stabilising switching sequences for a switched system constructed from a family of unstable linear subsystems and the construction of multiple polyhedral Lyapunov functions.

This paper proposes a new methodology for designing robust affine state-feedback control laws, so that wide-range safe and efficient operation of switched-mode DC-DC boost converters is guaranteed. Several undesirable nonlinear phenomena such as unstable attractors and subharmonic oscillations are avoided through bifurcation analysis based on the bilinear averaged model of the converter. The control design procedure also relies on constrained stabilization principles and the generation of safety domains using piecewise linear Lyapunov functions, so that robustness to supply voltage and output load variations is ensured, while input saturation is avoided and additional state constraints are also respected. The technique has been numerically and experimentally validated.

SUMMARYIn this paper the problem of estimating controllable and recoverable regions for classes of nonlinear systems in the presence of uncertainties, state and control constraints is considered. A new computational technique is proposed based upon a ray-gridding idea in contrast to the usual gridding techniques. The new technique is also based on the positive invariance principle and the use of piecewise linear (PL) Lyapunov functions to generate polytopic approximations to the controllable/recoverable region with arbitrary accuracy. Various types of stabilizing controllers achieving certain trade-o!s between robustness, performance and safety, while respecting state and control constraints, can be easily generated. The technique allows the approximation of nonlinear systems via piecewise linear uncertain models which reduces the conservatism associated with linear uncertain models.

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