On the quadratic stability of switched linear systems associated with symmetric transfer function matrices

Stochastic stability in terms of an associated transfer function matrix for some hybrid systems with Markovian switching

“…De…nition 3.1. [12] An m m rational transfer function matrix G(s) is said to be strictly positive real (SPR) if there exists a real scalar > 0 such that G(s) is analytic for Re(s)…”

“…with A r(t) = A + 1 N (1 r(t))BD 1 C and random signal r(t) 2 M = f1; 2; :::; N g. This system is represented schematically as We start a stochastic counterpart of the results obtained in [11] and [12] by considering a N states Markovian switched controller of the system in order to be able to perform some useful simulations, and prove stochastic stability under a Markovian transition rule rather than an arbitrary switching. Which means that we deal with the weaker notion of stability than the guaranteed one considered in [11].…”

“…([11] and [12]). The main contribution in this paper consists on the use of the stochastic machinery in order to obtain some quite new stochastic stability results under veri…able conditions on the parameters and dynamics of the considered Markovian switched controller systems, and to give the suitable form to make the system switch to a …nite number of states in a stochastic approach rather than two states in [11] and [12]. The justi…cation of existence of a Lyapunov function is based on the Kalman-Yakubovic-Popov lemma.…”

Reducing conservatism in robust stability analysis and stabilisation of arbitrary switched linear systems

“…So, a classical approach for stability analysis of arbitrary switched linear systems is to find a CLF for all subsystems. In many research work such as [11–14] and the references therein, stability analysis of switched linear systems under arbitrary switching has been investigated using CLF in the quadratic form. Expressing the stability conditions in terms of linear matrix inequalities (LMIs) is the main advantage of applying common quadratic Lyapunov function (CQLF).…”