On the left eigenstructure assignment and state feedback design

Kouhi, Y.; Bajçinca, Naim

doi:10.1109/acc.2011.5991532

Cited by 4 publications

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“…This specific class of switched systems has been motivated by the simple state-feedback control algorithms for single-input and multi-input systems based on the com mon left eigenstructure assignment approach, leading to constructive stability analysis methods, see [4], [5], [8]. In a further step we adopt results (see [6], [7]) on converse Lyapunov theorems about robust asymptotic stability of the solutions of differential inclusions involving a non-empty upper-semicontinuous compact and convex set-valued map in IRn.…”

Section: Introduction and Outlinementioning

confidence: 99%

Robust control of switched linear systems

Kouhi

Bajçinca

2011

IEEE Conference on Decision and Control and European Control Conference

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We consider robust control of switched linear systems under arbitrary time-dependent switching signals.First, we introduce a common quadratic Lyapunov function for the class of switched linear systems with Hurwitz constituent matrices in jRnxn sharing n -1 linearly independent common left eigenvectors. The common quadratic Lyapunov function is then used for robust stability analysis of the convexified differential inclusion associated with the underlying switched linear system. Finally, using the common left eigenstructure assignment approach for multi-input systems, robust design by means of state-feedback control is proposed.

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Section: Introduction and Outlinementioning

confidence: 99%

Robust control of switched linear systems

Kouhi

Bajçinca

2011

IEEE Conference on Decision and Control and European Control Conference

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“…Hence, an important related issue consists in the computation of a single proper eigenvector in R n which guarantees the simultaneous stability of all linear constituents at hand. To this end, tools for constructing a suitable eigenvector that stabilizes a given single linear system are pre-requisite, see [5,6]. This is thoroughly discussed in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Nonsmooth control design for stabilizing switched linear systems by left eigenstructure assignment

Kouhi

Bajçinca

2011

IFAC Proceedings Volumes

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Novel design algorithms for exponential stability of switched linear systems using the left eigenstructure assignment approach by state feedback control are proposed in this article. For given switching constraints in the state space R n , a state feedback controller for single-input switched systems is designed, based on the fact that closed loop system solutions are enforced to converge towards the invariant hyperplane attractor in R n , as defined by the imposed common left eigenvector. The latter is appropriately constructed to guarantee the simultaneous stabilization of all constituent linear sub-systems, and to avoid the intersection of the switching manifolds with its invariant attractor set. For arbitrary switching, a set of n linearly independent common left eigenvectors in R n is selected, introducing n hyperplane attractors, and n(n − 1) switching control hyperplane manifolds. The attrators are sequentially "turned on", in accordance with the switching event generated by the Filippov solutions upon hitting the underlying control manifolds. Thereby, an additional state feedback control action for a second input is designed, using the nonsmooth Lyapunov stability criteria to avoid sliding modes and guarantee exponential stability for the Filippov solutions.

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On Stabilization of Switched Linear MI Systems Using in Part Common Left Eigenvector Assignment Based on LMIs∗∗The work presented in this paper was supported by VEGA, the Grant Agency of the Ministry of Education and the Academy of Science of Slovak Republic, under Grant No. 1/0348/14. This support is very gratefully acknowledged.

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On the left eigenstructure assignment and state feedback design

Cited by 4 publications

References 1 publication

Robust control of switched linear systems

Robust control of switched linear systems

Nonsmooth control design for stabilizing switched linear systems by left eigenstructure assignment

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