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25
A loopedfunctional approach for robust stability analysis of linear impulsive systems
 Systems & Control Letters
, 2012
"... Abstract A new functionalbased approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces loopedfunctionals, considers nonmonotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate ..."
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Abstract A new functionalbased approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces loopedfunctionals, considers nonmonotonic Lyapunov functions and leads to LMIs conditions devoid of exponential terms. This allows one to easily formulate dwelltimes results, for both certain and uncertain systems. It is also shown that this approach may be applied to a wider class of impulsive systems than existing methods. Some examples, notably on sampleddata systems, illustrate the efficiency of the approach.
Robust stability of impulsive systems: A functionalbased approach
 in "4th IFAC conference on Analysis and Design of Hybrid Systems (ADHS’2012
, 2012
"... Abstract: An improved functionalbased approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov loopedfunctionals is provided. Looped functionals are peculiar functionals that allow to encode discretetime stability criteria into continuoustime conditions and t ..."
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Cited by 5 (3 self)
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Abstract: An improved functionalbased approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov loopedfunctionals is provided. Looped functionals are peculiar functionals that allow to encode discretetime stability criteria into continuoustime conditions and to consider nonmonotonic Lyapunov functions along the trajectories of the impulsive system. Unlike usual discretetime stability conditions, the obtained ones are convex in the system matrices, an important feature for extending the results to uncertain systems. It is emphasized in the examples that the proposed approach can be applied to a class of systems for which existing approaches are inconclusive, notably systems having unstable continuous and discrete dynamics.
Computing Upperbounds of the Minimum Dwell Time of Linear Switched Systems via Homogeneous Polynomial Lyapunov Functions
, 2010
"... This paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization based on LMIs. This sequence is obtained by adopting two p ..."
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Cited by 4 (0 self)
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This paper investigates the minimum dwell time for switched linear systems. It is shown that a sequence of upper bounds of the minimum dwell time can be computed by exploiting homogeneous polynomial Lyapunov functions and convex optimization based on LMIs. This sequence is obtained by adopting two possible representations of homogeneous polynomials, one based on Kronecker products, and the other on the square matrix representation. Some examples illustrate the use and the potentialities of the proposed approach.
Stabilization of Markovian systems via probability rate synthesis and output feedback
 IEEE Transactions on Automatic Control
"... Abstract—This technical note is concerned with the stabilization problem of Markovian jump linear systems via designing switching probability rate matrices and static outputfeedback gains. A novel necessary and sufficient condition is established to characterize the switching probability rate matr ..."
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Abstract—This technical note is concerned with the stabilization problem of Markovian jump linear systems via designing switching probability rate matrices and static outputfeedback gains. A novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of Markovian jump linear systems. Based on this, a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices. Extensions to the polytopic uncertain case are also provided. All the conditions are formulated in terms of linear matrix inequalities with some equality constraints, which can be solved by two modified cone complementarity linearization algorithms. Examples are given to show the effectiveness of the proposed method. Index Terms—Linear matrix inequality (LMI), Markovian process, output feedback, stabilization, switched system. I.
Stability and stabilizability of special classes of discretetime positive switched systems
, 2011
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Exponential Admissibility and Dynamic Output Feedback Control of Switched Singular Systems with Interval TimeVarying Delay
"... This paper is concerned with the problems of exponential admissibility and dynamic output feedback DOF control for a class of continuoustime switched singular systems with interval timevarying delay. A fullorder, dynamic, synchronously switched DOF controller is considered. First, by using the av ..."
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This paper is concerned with the problems of exponential admissibility and dynamic output feedback DOF control for a class of continuoustime switched singular systems with interval timevarying delay. A fullorder, dynamic, synchronously switched DOF controller is considered. First, by using the average dwell time approach, a delayrangedependent exponential admissibility criterion for the unforced switched singular timedelay system is established in terms of linear matrix inequalities LMIs . Then, based on this criterion, a sufficient condition on the existence of a desired DOF controller, which guarantees that the closedloop system is regular, impulse free and exponentially stable, is proposed by employing the LMI technique. Finally, some illustrative examples are given to show the effectiveness of the proposed approach.
Stabilization of ContinuousTime Switched Linear Positive Systems
"... AbstractIn this paper we considered a few problems related to linear positive switched systems. First, we provide a result on statefeedback stabilization of autonomous linear positive switched systems through piecewise linear copositive Lyapunov functions. This is accompanied by a side result on ..."
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AbstractIn this paper we considered a few problems related to linear positive switched systems. First, we provide a result on statefeedback stabilization of autonomous linear positive switched systems through piecewise linear copositive Lyapunov functions. This is accompanied by a side result on the existence of a switching law guaranteeing an upper bound to the optimal L1 cost. Then, the induced L1 guaranteed cost cost is tackled, through constrained piecewise linear copositive Lyapunov functions. The optimal L1 cost control is finally studied via Hamiltonian function analysis.
Stability analysis of a class of uncertain switched systems on time scale using Lyapunov functions
, 2015
"... a b s t r a c t This paper deals with the stability analysis of a class of uncertain switched systems on nonuniform time domains. The considered class consists of dynamical systems which commute between an uncertain continuoustime subsystem and an uncertain discretetime subsystem during a certain ..."
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a b s t r a c t This paper deals with the stability analysis of a class of uncertain switched systems on nonuniform time domains. The considered class consists of dynamical systems which commute between an uncertain continuoustime subsystem and an uncertain discretetime subsystem during a certain period of time. The theory of dynamic equations on time scale is used to study the stability of these systems on nonuniform time domains formed by a union of disjoint intervals with variable length and variable gap. Using the concept of common Lyapunov function, sufficient conditions are derived to guarantee the asymptotic stability of this class of systems on time scale with bounded graininess function. The proposed scheme is used to study the leaderfollower consensus problem under intermittent information transmissions.