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This article deals with the stability analysis of Lure type systems through aperiodic sampled‐data control laws, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped‐functionals, which depends on the nonlinearity and its slope, and on a generalized Lure type function, that is quadratic on both the states and the nonlinearity and has a Lure‐Postnikov integral term. On this basis, conditions in the form of linear matrix inequalities to certify global or regional asymptotic stability of the closed‐loop system are obtained. These conditions are then used in optimization problems for computing the maximum intersampling interval or the maximum sector bounds for which the stability of the sampled‐data closed‐loop system is guaranteed. Numerical examples to illustrate the results are provided. [ABSTRACT FROM AUTHOR]

This work addresses the stability analysis of sampled-data control systems subject to variable sampling intervals and input saturation. From a hybrid system representation, stability conditions based on quadratic timer-dependent Lyapunov functions are proposed. Considering affine and generic polynomial timer-dependence, these conditions are cast in semidefinite and sum-of-squares optimization problems to provide maximized estimates of the region of attraction or to provide a lower bound for the maximum allowable intersampling time considering a given set of admissible initial conditions. [ABSTRACT FROM AUTHOR]

This study investigates different observer architectures for the state estimation of linear aperiodic sampled-data systems and formally shows that a complex structure is not necessarily better than a simpler one with respect to the considered cost functional and to a class of timer-dependent Lyapunov functions. The work also shows how to design the state observer through sum of squares programming, presenting a numerical example. [ABSTRACT FROM AUTHOR]

This paper presents a new framework for stability assessment of discrete-time piecewise affine systems. An implicit representation for piecewise functions based on ramp nonlinearities is proposed. Instead of the usual sector inequalities adopted in the study of Lurie systems, we directly exploit properties of the ramp function, which are given by a particular set of identities and inequalities. These properties are then used to derive stability conditions associated to piecewise quadratic Lyapunov functions. These functions are implicitly defined from quadratic forms involving ramp functions. These conditions can be cast as LMIs and their numerical solution is illustrated by examples highlighting the advantages of the proposed method over existing stability analysis methods for PWA systems. [ABSTRACT FROM AUTHOR]