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138
Stability and Stabilizability of Switched Linear Systems: A Short Survey of Recent Results
, 2005
"... During the last decade, there has been increasing interest in the stability analysis and switching control design for switched linear systems. This paper aims to briefly survey recent results in this field, focusing on stability analysis and switching stabilization problems. First, the stability an ..."
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Cited by 110 (10 self)
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During the last decade, there has been increasing interest in the stability analysis and switching control design for switched linear systems. This paper aims to briefly survey recent results in this field, focusing on stability analysis and switching stabilization problems. First, the stability analysis problem for switched linear systems is reviewed. We focus on the asymptotic stability analysis for switched linear systems under arbitrary switching, and highlight necessary and sufficient conditions for this problem. Secondly, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. One of the most elusive problems in the switched systems literature has been the switching stabilizability problem, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Necessary and sufficient conditions for asymptotic stabilizability of switched linear systems are described.
A Clustering Technique for the Identification of Piecewise Affine Systems
, 2001
"... We propose a new technique for the identification of discretetime hybrid systems in the PieceWise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we provide an algorithm that ..."
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Cited by 95 (11 self)
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We propose a new technique for the identification of discretetime hybrid systems in the PieceWise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.
An Algebraic Geometric Approach to the Identification of a Class of Linear Hybrid Systems
 In Proc. of IEEE Conference on Decision and Control
, 2003
"... We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the ..."
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Cited by 57 (15 self)
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We propose an algebraic geometric solution to the identification of a class of linear hybrid systems. We show that the identification of the model parameters can be decoupled from the inference of the hybrid state and the switching mechanism generating the transitions, hence we do not constraint the switches to be separated by a minimum dwell time. The decoupling is obtained from the socalled hybrid decoupling constraint, which establishes a connection between linear hybrid system identification, polynomial factorization and hyperplane clustering. In essence, we represent the number of discrete states n as the degree of a homogeneous polynomial p and the model parameters as factors of p. We then show that one can estimate n from a rank constraint on the data, the coe#cients of p from a linear system, and the model parameters from the derivatives of p. The solution is closed form if and only if n 4. Once the model parameters have been identified, the estimation of the hybrid state becomes a simpler problem. Although our algorithm is designed for noiseless data, we also present simulation results with noisy data. 1
Observability and Identifiability of Jump Linear Systems
 In Proc. of IEEE Conference on Decision and Control
, 2002
"... We analyze the observability of the continuous and discrete states of a class of linear hybrid systems. We derive rank conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. We also study the identifiability of the mo ..."
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Cited by 53 (8 self)
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We analyze the observability of the continuous and discrete states of a class of linear hybrid systems. We derive rank conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. We also study the identifiability of the model parameters by characterizing the set of models that produce the same output measurements. Finally, when the data are generated by a model in the class, we give conditions under which the true model can be identified.
Identification of piecewise affine systems via mixedinteger programming
 AUTOMATICA
, 2004
"... This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (WPWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixedinteger linear or quadratic programming ..."
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Cited by 47 (5 self)
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This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes (HHARX) and Wiener piecewise affine (WPWARX) autoregressive exogenous models. In particular, we provide algorithms based on mixedinteger linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where switches occur only seldom in the estimation data, we also suggest a way of trading off between optimality and complexity by using a change detection approach.
A boundederror approach to piecewise affine system identification
 IEEE Transactions on Automatic Control
, 2005
"... Abstract — This paper proposes a threestage procedure for ..."
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Cited by 47 (1 self)
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Abstract — This paper proposes a threestage procedure for
Reachability and control synthesis for piecewiseaffine hybrid systems on simplices
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2006
"... In this paper, we consider the synthesis of control laws for piecewiseaffine hybrid systems on simplices. The construction is based on the solution to the controltofacet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit alg ..."
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Cited by 44 (0 self)
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In this paper, we consider the synthesis of control laws for piecewiseaffine hybrid systems on simplices. The construction is based on the solution to the controltofacet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit algorithm using only linear algebra and reachset computations for automata; no numerical integration is required. The method is conservative, in that it may fail to find a control law where one exists, but one cannot hope for a sharp algorithm for control synthesis since reachability for piecewiseaffine hybrid systems is undecidable.
Optimal controllers for hybrid systems: Stability and piecewise linear explicit form
 in Proceedings of the 39th IEEE Conference on Decision and Control
, 2000
"... In this paper we propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closedloop stability. Hybrid systems are modeled in discretetime within the mixed logical dynamical (MLD) framework[8], or, equivalently [7], as piecewise af ..."
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Cited by 43 (9 self)
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In this paper we propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closedloop stability. Hybrid systems are modeled in discretetime within the mixed logical dynamical (MLD) framework[8], or, equivalently [7], as piecewise affine (PWA) systems. A stabilizing controller is obtained by designing a model predictive controller (MPC), which is based on the minimization of a weighted 1/∞norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a mixedinteger linear program (MILP) which depends on the current state. Although efficient branch and bound algorithms exist to solve MILPs, these are known to be NPhard problems, which may prevent their online solution if the samplingtime is too small for the available computation power. Rather than solving the MILP on line, in this paper we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP (mpMILP). As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of the heat exchange system [16] shows the potential of the method.
Observability of Linear Hybrid Systems
 In Hybrid Systems: Computation and Control, LNCS
, 2003
"... We analyze the observability of the continuous and discrete states of continuoustime linear hybrid systems. For the class of jumplinear systems, we derive necessary and su#cient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms t ..."
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Cited by 42 (5 self)
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We analyze the observability of the continuous and discrete states of continuoustime linear hybrid systems. For the class of jumplinear systems, we derive necessary and su#cient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. Our conditions are simple rank tests that exploit the geometry of the observability subspaces. For linear hybrid systems, we derive weaker rank conditions that are su#cient to guarantee the uniqueness of the reconstruction of the state trajectory, even when the individual linear systems are unobservable.
OptimizationBased Verification and Stability Characterization of Piecewise Affine and Hybrid Systems
 In Hybrid Systems: Computation and Control
, 2000
"... In this paper, we formulate the problem of characterizing the stability of a piecewise affin (PWA) system as a verification problem. The basic idea is to take the whole R^n as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semiglobal ..."
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Cited by 40 (9 self)
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In this paper, we formulate the problem of characterizing the stability of a piecewise affin (PWA) system as a verification problem. The basic idea is to take the whole R^n as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semiglobal stability by restricting the set of initial conditions to an (arbitrarily large) bounded set X(0), and label as "asymptotically stable in T steps" the trajectories that enter an in variant set around the origin within a finite time T ,or as "unstable in T steps" the trajectories which enter a (very large) set X_inst . Subsets of X (0) leadin ton2W of the two previous cases are labeled as "nv classifiable in T steps". The domain of asymptotical stability in T steps is a subset of the domain of attraction ofan equilibrium poin t, an has the practicalmeanca of collectin inPv)v convW2xvP from which the settlin time of the system is smaller than T . In addition it can be computed algorithmically i...