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...ic Hybrid Systems Different modelling paradigms for SHS have been proposed in literature [20], [2]. Applications of SHS range from air traffic management [23], biology [18], to communication networks =-=[19]-=-. Formally, a stochastic hybrid automaton (SHA) is defined as a tuple H = (Q,X , F,R, λ) has been defined in [8], [7]. The executions of an SHA,H , can be described as follows: start with an initial p...

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...) Example 4. Consider the general uncertain model (1) with a12 ∈ [−5, −1], a21 ∈ [2, 4], a22 ∈ [−0.6, 0.6]. Find values of the coefficient a11 for which the model is robustly stable. In this case from (29) we have α−12 = −20, α + 12 = −2. Because α+12 < 0 and (30) holds, we apply condition (41) of Lemma 4. From this condition we have that the model is robustly stable if and only if a+11 < α − 12/(a − 22+1) = −20/0.4 = −50. The same result one obtains from Algorithm 1. Example 5. Find values of the coefficient a11 for which is robustly stable the positive uncertain general model (1) with a12 ∈ [1, 4], a21 ∈ [2, 6] and a22 ∈ [0, 0.5]. From (29) and Theorem 9 we obtain α− 12 = 2, α+ 12 = 24 and a+11 < −24/0.5 = −48. This means that the positive model is robustly stable if and only if a11 ∈ (−∞, −48). The same result one obtains from Algorithm 1. 4. Concluding remarks Simple analytical conditions for stability and for robust stability of the new general 2D model (1) of scalar continuousdiscrete linear systems, standard and positive, have been given. These conditions are expressed in terms of the coefficients of the model. In particular it has been shown that: • the general model (1) is asymp...

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...diffusion process e is defined by (LV )(e) := lim t→s E � V (e(t)|e(s) = e � − V (e) , ∀e ∈ R t − s n , t > s ≥ 0, (21) where E � V (e(t)|e(s) = e � denotes the expectation of V (e(t)) given e(s) = e =-=[15, 5]-=-. The generator for the jump diffusion process described by (18) is given by LV (e) = ∂V (e) ∂V (e) ∂e · Ae + 1 2 tr � σ ′ ∂2V (e) σ ∂e2 � � + λ(e) � � V (ζ) dµ(ζ) − V (e) , (22) where ∂e ∂e2 denote t...

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...analysis, and arrive at the results directly by employing what we think are less involved and more intuitively appealing techniques. Existing work on stability of stochastic switched systems includes =-=[23, 28, 27, 5, 3, 9, 11, 15, 14, 1]-=-; see also [6, Chapter 1] for a survey techniques employed in these articles. Analysis results obtained via our approach, including those reported in our earlier article [7] where each subsystem was r...

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...e Markov chains. However, the rate at which these transitions occur may depend on the continuous-state. The model used here for SHSs, whose formal definition can be found in Sec. 2, was introduced in =-=[1]-=- and is heavily inspired by the Piecewise-Deterministic Markov Processes (PDPs) in [2]. Alternative models can be found in [3,4,5]. The extended generator of a stochastic hybrid system allows one to c...