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This paper establishes exponential convergence rates for a class of primal–dual gradient algorithms in distributed optimization without strong convexity. The convergence analysis is based on a carefully constructed Lyapunov function. By evaluating metric subregularity of the primal–dual gradient map, we present a general criterion under which the algorithm achieves exponential convergence. To facilitate practical applications of this criterion, several simplified sufficient conditions are derived. We also prove that although these results are developed for the continuous-time algorithms, they carry over in a parallel manner to the discrete-time algorithms constructed by using Euler's approximation method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the LQG design for linear system to the case of switched linear systems in continuous time. The main result provides a control Lyapunov function and a dynamic output feedback law leading to sub-optimal solutions. Practically, the dynamic output feedback is easy to apply and the design procedure is effective if there exists at least one controllable and observable convex combination of the subsystems. Practical applications concern the large class of power converters. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problems of robust and  filtering for 2-dimensional (2-D) discrete-time linear systems described by a Fornasini–Marchesini second model with matrices that depend affinely on convex-bounded uncertain parameters. By a suitable transformation, the system is represented by an equivalent difference-algebraic representation. A parameter-dependent Lyapunov function approach is then proposed for the design of 2-D stationary discrete-time linear filters that ensure either a prescribed performance or  performance for all admissible uncertain parameters. The filter designs are given in terms of linear matrix inequalities. Numerical examples illustrate the effectiveness of the proposed filter design methods. [Copyright &y& Elsevier]

This paper treats the control design of a state-dependent switching function for discrete-time switched affine systems, assuring global asymptotic stability of a limit cycle. This limit cycle is determined according to criteria of interest related to the steady-state behaviour of the system trajectories, as for instance, its mean value, oscillation amplitude and frequency. More specifically, based on a time-varying convex Lyapunov function, a min-type switching rule is determined in order to orchestrate the state trajectories, evolving from any initial condition, towards the desired limit cycle. Most of the available methodologies are able to guide the state trajectories to a set of attraction containing the equilibrium point, assuring its practical stability. However, although important, the behaviour of the trajectories inside this set is not considered. Differently, the proposed technique assures an appropriate steady-state behaviour by adequately designing the limit cycle. Moreover, the proposed conditions take into account H 2 and H ∞ guaranteed costs, assuring also a suitable transient response. All the conditions are expressed in terms of linear matrix inequalities being simple to solve by readily available tools. Illustrative examples, one of them concerning the voltage regulation of a DC–DC multicellular converter, are used for validation and comparison. [ABSTRACT FROM AUTHOR]