Stability and stabilization of piecewise affine and hybrid systems: an LMI approach

Mignone, D.; Ferrari-Trecate, Giancarlo; Morari, Manfred

doi:10.1109/cdc.2000.912814

Cited by 182 publications

(150 citation statements)

References 9 publications

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“…It can be used to make 2 M. DI BERNARDO, U. MONTANARO, J. M. OLM, S. SANTINI a PWL plant track asymptotically the states of a smooth or PWL reference model. As shown in the paper, a proof of asymptotic stability can be obtained in both cases under the assumption that the reference model is quadratically stable (Q-stable) [11], that is, it admits a common quadratic Lyapunov function when unforced. Indeed, when this is verified, it is possible to follow the steps of Landaus' passivity-based classical proof and recast the closed-loop error system as a feedback system.…”

Section: Introductionmentioning

confidence: 99%

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Model reference adaptive control of discrete‐time piecewise linear systems

Bernardo

Montanaro

Olm

et al. 2012

Intl J Robust & Nonlinear

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SUMMARYThis article presents a switched MRAC controller for discrete-time piecewise linear systems. In the spirit of the work by Landau [1], the proof of asymptotic stability of the corresponding closed-loop error is carried out recasting its dynamics as a feedback system and showing the appropriate passivity features of the feedforward and the feedback paths. The challenge lies on the fact that both loops can be piecewise linear. Numerical results show excellent performance of the proposed controller even in the face of sudden variations of the plant parameters.

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Section: Introductionmentioning

confidence: 99%

“…Assume that the reference model (3) is PWQ-stable [11], i.e. there exists a set of symmetric, positive definite matrices P i > 0, for all i ∈ M, such that the following LMI is verified:…”

Section: Theoremmentioning

confidence: 99%

Model reference adaptive control of discrete‐time piecewise linear systems

Bernardo

Montanaro

Olm

et al. 2012

Intl J Robust & Nonlinear

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“…In the case of discrete time, the authors of [10] presented an approach for stabilization of piecewise linear systems based on a global quadratic Lyapunov function. In [5,11], the authors gave a number of results on stability analysis, controller design, analysis, and controller design for the piecewise linear systems based on a piecewise Lyapunov function. In [5], for control synthesis, the affine term was treated as a disturbance.…”

Section: Introductionmentioning

confidence: 99%

H∞ Fault Tolerant Control of WECS Based on the PWA Model

et al. 2014

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Abstract:The main contribution of this paper is the development of fault tolerant control for a wind energy conversion system (WECS) based on the stochastic piecewise affine (PWA) model. In this paper the normal and fault stochastic PWA models for WECS including multiple working points at different wind speeds are established. A reliable piecewise linear quadratic regulator state feedback is designed for the fault tolerant actuator and sensor. A sufficient condition for the existence of the passive fault tolerant controller is derived based on some linear matrix inequalities (LMIs). It is shown that the fault tolerant controller of WECS can control the wind turbine exposed to multiple simultaneous sensor faults or actuator faults; that is, the reliability of wind turbines can be improved.

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“…However, the problem is that is not clear how the nonincreasing sequence can be effectively checked in general, since it would in principle require checking all possible behaviours of a hybrid system. This problem has been tackled by constructing Lyapunov functions that are either piecewise linear (Koutsoukos and Antsaklis, 2001) or piecewise quadratic (Pettersson and Lennartson, 1996;Johansson and Rantzer, 1998;Mignone et al, 2000). In the latter case the piecewise quadratic function should be continuous on the switching boundaries, which can be checked efficiently by solving a linear matrix inequality.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis for Hybrid Automata Using Conservative Gains

Langerak

Polderman

Krilavičius

2003

IFAC Proceedings Volumes

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This paper presents a stability analysis approach for a class of hybrid automata. It is assumed that the dynamics in each location of the hybrid automaton is linear and asymptotically stable, and that the guards on the transitions are hyperplanes in the state space. For each pair of ingoing and outgoing transitions in a location a conservative estimate is made of the gain via a Lyapunov function for the dynamics in that location. It is shown how the choice of the Lyapunov function can be optimized to obtain the best possible estimate. The calculated conservative gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton.

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Stability and stabilization of piecewise affine and hybrid systems: an LMI approach

Cited by 182 publications

References 9 publications

Model reference adaptive control of discrete‐time piecewise linear systems

Model reference adaptive control of discrete‐time piecewise linear systems

H∞ Fault Tolerant Control of WECS Based on the PWA Model

Stability Analysis for Hybrid Automata Using Conservative Gains

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