New robust stable MPC using linear matrix inequalities

Abstract

This paper addresses the stability of Model Predictive Control (MPC) with output feedback. The proposed controller uses a new state-space formulation of the system, and the control problem is presented as an LMI optimization problem. The stability condition for the closed loop is included as a Lyapunov inequality. The resulting optimization problem becomes nonlinear with the inclusion of the stabilizing condition. A suboptimal solution is developed and the problem reduces to a pair of coupled LMI problems. An iterative solution that converges to a stable output feedback gain is proposed. A polytopic set of process models can be considered. A simulation example is included in the paper and shows that the proposed strategy eliminates the usual practice of enforcing robustness by detuning the MP controller

Exponential Stability of Coupled Systems on Networks with Mixed Delays and Reaction-Diffusion Terms

“…Recently, attention was paid to stability analysis for coupled systems increasingly, and many methods were proposed. Gan and Xu [8] discussed the local stability by analyzing the corresponding characteristic equations, and more scholars [5,[20][21][22] used linear matrix inequality approach to construct the Lyapunov function of a system. As is well-known to us, it is a challenging task to construct an appropriate Lyapunov function.…”

“…In [19], some new delay-dependent conditions are derived applying the Lyapunov stability theory, Dynkins formula, and linear matrix inequality technique. And the method, linear matrix inequalities technique, is also used in the paper [20]. So far, plenty of sufficient conditions have been deduced to determine the stability of coupled systems and more relevant researches can be seen in [21,22] and the references therein.…”

Input-to-state stability of multi-group stochastic coupled systems with time-varying delay

“…However, because of the complexity for coupled systems, there is no doubt that constructing a proper Lyapunov function for a given coupled system is rather difficult. Some scholars established several Lyapunov functions for some certain coupled systems successfully by using the linear matrix inequality and obtained many achievements (see [28,29]). In recent few years, Li et al utilized the graph-theoretic approach to derive the construction of Lyapunov function for some multi-group coupled systems and further made a study of global stability [30].…”

A new method for exponential stability of coupled reaction–diffusion systems with mixed delays: Combining Razumikhin method with graph theory

“…Abundant approaches have been come up with, such as the Lyapunov method [10], linear matrix inequalities approach [12][13][14][15], and various kinds of control like adaptive control [16][17][18], impulsive control [19]. The Razumikhin method is also commonly used.…”