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In this article, three different types of stochastic asymptotic stability for nonlinear stochastic semi‐Markov jump systems (SSMJS) are investigated. Novel sufficient conditions for p$$ p $$th (p>0)$$ \left(p>0\right) $$‐moment asymptotic stability, almost sure asymptotic stability and stochastic asymptotic stability in the large are obtained. It is remarkable that the obtained results in the latter case cover the results in existing literature. Finally, two examples are presented to confirm the validity of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete-time domains. A particular class of matrix inequalities, the so-called Lyapunov--Metzler inequalities, provides conditions for open-loop stability analysis and closed-loop switching control using state and output feedback. Switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations. Lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the Hamilton--Jacobi--Bellman inequality. An upper bound on the optimal cost associated with a closed-loop stabilizing switching strategy is provided as well. The solution of the output feedback problem is based on the construction of a full-order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule. Throughout, the theoretical results are illustrated by means of academic examples. A realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported. Index Terms--Linear matrix inequalities (LMIs), output feedback control, switched systems.

Efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H{infinity} filtering Riccati equation. This provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.

The finite-horizon [H.sub.[infinity]] filtering and prediction problems in the discrete-time case admit solutions only if a suitable difference Riccati equation is solved by a matrix sequence satisfying "feasibility" conditions. In this work, sufficient conditions ensuring the existence of filters and predictors over an arbitrarily long time interval are derived. Moreover, it is shown that, under these conditions, finite horizon estimators tend to stable stationary ones as the time horizon increases. Index Terms - [H.sub.[infinity]] filtering, [H.sub.[infinity]] prediction, Riccati equations.

This paper considers linear systems which are positively invariant in a second-order cone (ice-cream cone). Three problems are addressed: (i) stability; (ii) L 1 performance; (iii) state feedback design for stabilisation and optimal L 1 performance while preserving cone invariance. We derive necessary and sufficient conditions via Linear Matrix Inequalities (LMI) for the solution of problems (i) and (ii). As for problem (iii), a full parametrization of feasible state feedback gains is provided, along with some LMI relaxations useful to compute a feasible gain. Finally, a numerical example is briefly discussed. [ABSTRACT FROM AUTHOR]