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Robust stabilisation problem of discrete-time switched linear systems with bounds on the controls and states is investigated in this study. Firstly, the controller synthesis for systems with interval uncertainties which guarantees positivity and stability of the closed-loop system is studied. These results are then extended to the systems with polytopic uncertainties. All the conditions are formulated in terms of linear feasibility. Finally, numerical examples illustrate the effectiveness of the proposed methods.

In this study, a time optimisation problem is solved for a class of linear time-invariant switched stochastic systems with multi-switching times using the calculus of variations. The objective of authors’ study is to minimise a cost functional defined on the system state, where the sequence of active subsystems is pre-specified and the switching times are the only control variables. The gradient of the cost functional with respect to the switching times is derived, which has an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instants. The proposed method is applied on a two-tank system, which is a practical example of switched systems. Combining with another numerical example with three switching times case, the viability of the proposed method is further demonstrated.

A robust output feedback tracking strategy for uncertain nonlinear systems with output measurement noise is presented by using a passivity approach. The control algorithm guarantees boundedness of all the signals in the whole closed-loop system. Tracking accuracy can be reduced to a desirable bound. A simulation example is included to demonstrate effectiveness of the proposed algorithm.