Paolo Bolzern

This paper deals with the analysis of stability and the characterisation of input–output norms for discrete-time periodic switched linear systems. Such systems consist of a network of time-periodic linear subsystems sharing the same state vector and an exogenous switching signal that triggers the jumps between the subsystems. The overall system exhibits a complex dynamic behaviour due to the interplay between the time periodicity of the subsystem parameters and the switching signal. Both arbitrary switching signals and signals satisfying a dwell-time constraint are considered. Linear matrix inequality conditions for stability and guaranteed H₂ and H_∞ performances are provided. The results heavily rely on the merge of the theory of linear periodic systems and recent developments on switched linear time-invariant systems.

This paper generalises the Small Gain Theorem – SGT to cope with switched linear systems. A switching strategy able to guarantee stability of the feedback interconnection of a switching linear subsystem and a linear stable norm-bounded perturbation is developed. The new version of SGT is specially important to solve two different problems. The first one concerns the possibility of enhancing the robustness of a feedback control system by appropriately orchestrating the switches among a set of given linear regulators. The second problem is the design of a stabilising switching strategy for time-delay switched systems. Both cases of state and output feedback switching laws are considered. Remarkably, since the sufficient conditions for the existence of a solution are delay-dependent, they are less conservative with respect to previous results in the literature. The theory is illustrated by means of academic examples.

This paper deals with the notion of almost sure stability for linear stochastic systems whose dynamic matrix depends on an ergodic process. It is shown that such systems are exponentially almost surely stable if and only if their transition matrix is averagely contractive over a finite, yet unknown, time interval. In order to test this condition, an efficient computational procedure based on a Monte Carlo strategy is proposed. Moreover, an H_∞ condition ensuring exponential almost sure stability is proven. The condition requires that the mean square value of the ergodic process is less than a constant involving the H_∞-norm of an appropriate transfer function. The applicability of the proposed methods is illustrated by means of a numerical example.

This paper deals with the notion of almost sure stability for linear stochastic systems whose dynamic matrix depends on an ergodic process. It is shown that such systems are exponentially almost surely stable if and only if their transition matrix is averagely contractive over a finite, yet unknown, time interval. In order to test almost sure stability, an efficient computational procedure based on a Monte Carlo strategy is proposed. The applicability of the proposed method is illustrated by means of a numerical example

The paper deals with special classes ofH_∞estimation problems, where the signal to be estimated coincides with the uncorrupted measured output. Explicit bounds on the difference between nominal and actualH_∞performance are obtained by means of elementary algebraic manipulations. These bounds are new in continuous‐time filtering and discrete‐time one‐step ahead prediction. As for discrete‐time filtering, the paper provides new proofs that are alternative to existing derivations based on the Krein spaces formalism. In particular, some remarkableH_∞robustness properties of Kalman filters and predictors are highlighted. The usefulness of these results for improving the estimator design under a mixedH₂/H_∞viewpoint is also discussed. The dualization of the analysis allows one to evaluate guaranteedH_∞robustness bounds for state‐feedback regulators of systems affected by actuator disturbances. Copyright © 2001 John Wiley & Sons, Ltd.