On infinity norms as Lyapunov functions for piecewise affine systems

Lazar, Mircea and Jokić, Andrej (2010) On infinity norms as Lyapunov functions for piecewise affine systems. = On infinity norms as Lyapunov functions for piecewise affine systems. In: 13th ACM International Conference on Hybrid Systems: Computation and Control, HSCC'10, 12-15.04.2010., Stockholm, Sweden.

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Official URL: https://dl.acm.org/citation.cfm?id=1755972

Abstract

This paper considers off-line synthesis of stabilizing static feedback control laws for discrete-time piecewise affine (PWA) systems. Two of the problems of interest within this framework are: (i) incorporation of the S-procedure in synthesis of a stabilizing state feedback control law and (ii) synthesis of a stabilizing output feedback control law. Tackling these problems via (piecewise) quadratic Lyapunov function candidates yields a bilinear matrix inequality at best. A new solution to these problems is proposed in this work, which uses infinity norms as Lyapunov function candidates and, under certain conditions, requires solving a single linear program. This solution also facilitates the computation of piecewise polyhedral positively invariant (or contractive) sets for discrete-time PWA systems.

Item Type: Conference or Workshop Item (Lecture)
Keywords (Croatian): bilinear matrix inequality; discrete-time; infinity norm; infinity norms; linear programs; new solutions; output feedback; output feedback controls; piece-wise; piecewise affine systems; quadratic Lyapunov function; S-procedures; stabilizing state; static feedback control; differential equations; electric grounding; feedback; feedback control; hybrid computers; hybrid systems; Lyapunov functions; Lyapunov methods; state feedback; synthesis (chemical); system stability; discrete time control systems
Subjects: NATURAL SCIENCES > Mathematics
TECHNICAL SCIENCE > Mechanical Engineering
TECHNICAL SCIENCE > Basic technical sciences
Divisions: 900 Department of Robotics and Production System Automation > 910 Chair of Engineering Automation
Indexed in Web of Science: No
Indexed in Current Contents: No
Date Deposited: 10 Jul 2015 08:35
Last Modified: 19 Nov 2018 12:48
URI: http://repozitorij.fsb.hr/id/eprint/4589

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