Matrix Inequality Based Design Method Research Articles

An H∞Output Feedback Control for Uncertain Singularly Perturbed T-S Fuzzy Systems

This paper deals with an <TEX>$H_{\infty}$</TEX> output feedback controller design for uncertain singularly perturbed T-S fuzzy systems. Integral quadratic constraints are used to describe various kinds of uncertainties of the plant. It is shown that the <TEX>$H_{\infty}$</TEX> norm of the uncertain singularly perturbed fuzzy system is less than <TEX>$\gamma$</TEX> for a sufficiently small <TEX>$\varepsilon$</TEX> > 0 if the <TEX>$H_{\infty}$</TEX> norms of both the slow and fast subsystem are less than <TEX>$\gamma$</TEX>. Using this fact, we develop a linear matrix inequality based design method which is independent of the singular perturbation parameter <TEX>$\varepsilon$</TEX>. A numerical example is provided to demonstrate the efficacy of the proposed design method.

A matrix inequality based design method for consensus problems in multi-agent systems

A matrix inequality based design method for consensus problems in multi-agent systemsIn this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.

Design of stabilizing control laws for second-order switched systems

In this paper, we design asymptotically stabilizing switching control laws for switched systems consisting of several second-order LTI subsystems with unstable foci. Switching is needed for the stabilization of a system consisting of several subsystems if each of its subsystems is unstable. We first study switched systems consisting of two subsystems with unstable foci and conic switching stabilizing control laws are derived. Then the result is extended to several subsystems. In particular, necessary and sufficient conditions for the asymptotic stabilizability of a switched system are derived. If the switched system is asymptotically stabilizable, an asymptotically stabilizing switching law can also be obtained. Finally, we briefly compare the method derived here to a matrix inequality based design method.