Control of Linear Switched Systems With Receding Horizon Modal Information

Essick, Ray; Lee, Jiwoong; Dullerud, Geir E.

doi:10.1109/tac.2014.2321251

Cited by 38 publications

(35 citation statements)

References 34 publications

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“…Multiple Lyapunov functions (see [5,10,20]) arise as an alternative to common Lyapunov functions. In the case of linear systems, the multiple quadratic Lyapunov functions such as those introduced in [3,7,8,15] hold special interest as checking for their existence boils down to solving a set of LMIs. The general framework of Path-Complete Lyapunov functions was recently introduced in [1] in this context, for analyzing and unifying the approaches cited above.…”

Section: Introductionmentioning

confidence: 99%

Path-Complete Graphs and Common Lyapunov Functions

Angeli

Αθανασόπουλος

Jungers

et al. 2017

Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control

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A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called its pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time switching systems under arbitrary switching. In this paper, we prove that the satisfiability of such a criterion implies the existence of a Common Lyapunov Function, expressed as the composition of minima and maxima of the pieces of the Path-Complete Lyapunov function. The converse, however, is not true even for discrete-time linear systems: we present such a system where a max-of-2 quadratics Lyapunov function exists while no corresponding PathComplete Lyapunov function with 2 quadratic pieces exists. In light of this, we investigate when it is possible to decide if a Path-Complete Lyapunov function is less conservative than another. By analyzing the combinatorial and algebraic structure of the graph and the pieces respectively, we provide simple tools to decide when the existence of such a Lyapunov function implies that of another.

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Section: Introductionmentioning

confidence: 99%

Path-Complete Graphs and Common Lyapunov Functions

Angeli

Αθανασόπουλος

Jungers

et al. 2017

Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control

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“…[8], [23]). Nevertheless, several tools have been developed, which provide semialgorithms to decide asymptotic stability [5]- [7], [14], [25], [30], [31], [33].…”

Section: Introductionmentioning

confidence: 99%

“…Here again, multiple quadratic Lyapunov functions such as those introduced in [7], [12], [14], [25] hold special interest because checking for their existence also amounts to solving a set of linear matrix inequalities. For example, let us consider a switching System (1) on M = 2 modes.…”

Section: Introductionmentioning

confidence: 99%

On Path-Complete Lyapunov Functions: Geometry and Comparison

Philippe

Αθανασόπουλος

Angeli

et al. 2019

IEEE Trans. Automat. Contr.

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“…Nevertheless, several analysis and control techniques have been devised (see e.g. [11], [19]- [21]), often providing conservative yet tractable methods. The particular question of the stability of a switched system attracts a lot of attention; in the past few years, approaches using multiple Lyapunov functions have been devised [4], [8], [21], with recent works [1], [12], [28] analyzing how conservative these methods are.…”

Section: Introductionmentioning

confidence: 99%

Extremal storage functions and minimal realizations of discrete-time linear switching systems

Philippe

Essick

Dullerud

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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We study the Lp induced gain of discretetime linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every p ≥ 1, the Lp-gain is exactly characterized through switching storage functions. These functions are shown to be the pth power of a norm. In order to consider general systems, we provide an algorithm for computing minimal realizations. These realizations are rectangular systems, with a state dimension that varies according to the mode of the system. We apply our tools to the study on the of L2-gain. We provide algorithms for its approximation, and provide a converse result for the existence of quadratic switching storage functions. We finally illustrate the results with a physically motivated example.

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Control of Linear Switched Systems With Receding Horizon Modal Information

Cited by 38 publications

References 34 publications

Path-Complete Graphs and Common Lyapunov Functions

Path-Complete Graphs and Common Lyapunov Functions

On Path-Complete Lyapunov Functions: Geometry and Comparison

Extremal storage functions and minimal realizations of discrete-time linear switching systems

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