In this paper we address the problem of optimal switching for switched linear systems. The uniqueness of our approach lies in describing the switching action by multiple control inputs. This allows us to embed the switched system in a larger family of systems and apply Pontryagin’s Minimum Principle for solving the optimal control problem. This approach imposes no restriction on the switching s...

The paper presents a combined power amplifier system consisting of a linear amplifier unit with a switched-mode (class D) current dumping stage arranged in parallel. With this topology the fundamental drawback of conventional linear power amplifiers the high loss is avoided. Compared to a pure class D (switching) amplifier the presented system needs no output filter to reduce the switching freq...

A polynomial approach to deal with the stability analysis of switched non-linear systems under arbitrary switching using dissipation inequalities is presented. It is shown that a representation of the original switched problem into a continuous polynomial system allows us to use dissipation inequalities for the stability analysis of polynomial systems. With this method and from a theoretical po...

In 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 ...

The paper represents the first part of a series of papers on realization theory of switched systems. Part I presents realization theory of linear switched systems, Part II presents realization theory of bilinear switched systems. More precisely, in Part I necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a linear switched system and a chara...

This paper considers the stabilization of planar switched linear control systems. First, a structure property of not completely controllable pair (A, b) is revealed. Based on it, a simply verifiable, necessary and sufficient condition for the planar switched linear control system to be feedback stabilizable, is presented under the assumption that the switching law is designable. The proof provi...

In this paper the discretization of switched and non-switched linear positive systems using Padé approximations is considered. We show: 1) diagonal Padé approximations preserve both linear and quadratic co-positive Lyapunov functions; 2) positivity need not be preserved even for arbitrarily small sampling time for certain Padé approximations. Sufficient conditions on the Padé approximations are...

This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations or configurations which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with re...

In this paper, the problem of H∞ filtering for a class of discrete-time switched systems with unknown inputs is investigated. By using switched Lyapunov functionals, sufficient conditions for the solution of this problem are obtained in terms of linear matrix inequalities (LMIs). Filtering is envisaged both with proportional and proportional integral observers. In addition, the results obtained...

This paper describes a design problem of the controller in switched systems. A switched system is a hybrid dynamical system consisting of continuous-time subsystems and a rule that controls the switching between them. The uncertainties of stability in the switching surface is a very sufficient problem in designing a switching-type controller. The stability analysis in the switching surface and ...