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Stabilization of discretetime switched linear systems: A controlLyapunov . . .
 AUTOMATICA, 45(11):2526
, 2009
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Chemical networks with inflows and outflows: A positive linear differential inclusions approach
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Formal modelling, analysis and verification of hybrid systems
 In Unifying Theories of Programming and Formal Engineering Methods, volume 8050 of LNCS
, 2013
"... Abstract. Hybrid systems is a mathematical model of embedded systems, and has been widely used in the design of complex embedded systems. In this chapter, we will introduce our systematic approach to formal modelling, analysis and verification of hybrid systems. In our framework, a hybrid system i ..."
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Abstract. Hybrid systems is a mathematical model of embedded systems, and has been widely used in the design of complex embedded systems. In this chapter, we will introduce our systematic approach to formal modelling, analysis and verification of hybrid systems. In our framework, a hybrid system is modelled using Hybird CSP (HCSP), and specified and reasoned about by Hybrid Hoare Logic (HHL), which is an extension of Hoare logic to hybrid systems. For deductive verification of hybrid systems, a complete approach to generating polynomial invariants for polynomial hybrid systems is proposed; meanwhile, a theorem prover for HHL that can provide tool support for the verification has been implemented. We give some case studies from realtime world, for instance, Chinese HighSpeed Train Control System at Level 3 (CTCS3). In addition, based on our invariant generation approach, we consider how to synthesize a switching logic for a considered hybrid system by reduction to constraint solving, to meet a given safety, liveness, optimality requirement, or any of their combinations. We also discuss other issues of hybrid systems, e.g., stability analysis.
Finiteness property of a bounded set of matrices with uniformly subperipheral spectrum
 J. Commun. Technol. Electron
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Optimal switching control design for polynomial systems: an LMI approach
, 2013
"... We propose a new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints. We formulate the switching design problem as an optimal control problem which is then relaxed to a linear programming (LP) problem in the space of occupation measures. ..."
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We propose a new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints. We formulate the switching design problem as an optimal control problem which is then relaxed to a linear programming (LP) problem in the space of occupation measures. This infinitedimensional LP can be solved numerically and approximately with a hierarchy of convex finitedimensional LMIs. In contrast with most of the existing work on LMI methods, we have a guarantee of global optimality, in the sense that we obtain an asympotically converging (i.e. with vanishing conservatism) hierarchy of lower bounds on the achievable performance. We also explain how to construct an almost optimal switching sequence. 1
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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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.
Explicit Construction of a Barabanov Norm for a Class of Positive Planar Discrete–Time Linear Switched Systems ⋆
"... We consider the stability under arbitrary switching of a discrete–time linear switched system. A powerful approach for addressing this problem is based on studying the “most unstable ” switching law (MUSL). If the solution of the switched system corresponding to the MUSL converges to the origin, the ..."
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We consider the stability under arbitrary switching of a discrete–time linear switched system. A powerful approach for addressing this problem is based on studying the “most unstable ” switching law (MUSL). If the solution of the switched system corresponding to the MUSL converges to the origin, then the switched system is stable for any switching law. The MUSL can be characterized using optimal control techniques. This variational approach leads to a Hamilton–Jacobi–Bellman equation describing the behavior of the switched system under the MUSL. The solution of this equation is sometimes referred to as a Barabanov norm of the switched system. Although the Barabanov norm was studied extensively, it seems that there are few examples where it was actually computed in closed–form. In this paper, we consider a special class of positive planar discrete– time linear switched systems and provide a closed–form expression for a corresponding Barabanov norm and a MUSL. The unit circle in this norm is a parallelogram.
On new sufficient conditions for stability of switched linear systems
, 2009
"... This work aims to connect two existing approaches to stability analysis of switched linear systems: stability conditions based on commutation relations between the subsystems and stability conditions of the slowswitching type. The proposed sufficient conditions for stability have an interpretation ..."
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Cited by 4 (1 self)
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This work aims to connect two existing approaches to stability analysis of switched linear systems: stability conditions based on commutation relations between the subsystems and stability conditions of the slowswitching type. The proposed sufficient conditions for stability have an interpretation in terms of commutation relations; at the same time, they involve only elementary computations of matrix products and induced norms, and possess robustness to small perturbations of the subsystem matrices. These conditions are also related to slow switching, in the sense that they rely on the knowledge of how slow the switching should be to guarantee stability; however, they cover situations where the switching is actually not slow enough, by accounting for relations between the subsystems. Numerical examples are included for illustration.