Average flow constraints and stabilizability in uncertain production-distribution systems

We consider a multi-inventory system with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first-order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of two requirements: (i) meeting any possible demand at each time (worst case stability) or (ii) achieving a predefined flow in the average (average flow constraints). Necessary and sufficient conditions for the achievement of both goals have been proposed by the authors. In this paper, we face the case in which these conditions are not satisfied. We show that, if we ignore the requirement on worst case stability, we can find a control strategy driving the expected value of the state to zero. On the contrary, if we ignore the average flow constraints, we can find a control strategy that satisfies worst case stability while optimizing any linear cost on the average control. In the latter case, we provide a tight bound for the cost

Integral Sliding Mode Control for Markovian Jump T-S Fuzzy Descriptor Systems Based on the Super-Twisting Algorithm

This paper investigates integral sliding mode control problems for Markovian jump T-S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analyzed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed

Robust ?? control of descriptor discrete-time Markovian jump systems

This paper considers the stochastic stability and the robust control of descriptor discrete-time systems with Markovian jumping parameters. In terms of linear matrix inequalities, a necessary and sufficient condition is proposed, which ensures a discrete-time descriptor Markovian jump system to be regular, causal and stochastically stable. A robust admissibility condition and a robust bounded real lemma are also developed. Based on these, a sufficient condition on the existence of a state-feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique. A robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed approach