Stabilization of constrained linear systems via smoothed truncated ellipsoids
نویسندگان
چکیده
Polyhedral Lyapunov functions are convenient to solve the constrained stabilization problem of linear systems as non-conservative estimates of the domain of attraction can be obtained. Alternatively, truncated ellipsoids can be used to find an under-estimate of the feasible region, with a considerably reduced number of parameters. This paper reformulates classic geometric intersection operators in terms of R-functions, leading to a new family of smooth Lyapunov functions. This approach can be used to smooth both polyhedral and truncated ellipsoids Lyapunov functions improving control performances, as shown in several benchmark examples.
منابع مشابه
A new class of Lyapunov functions for the constrained stabilization of linear systems
The constrained stabilization of linear uncertain systems is investigated via the set-theoretic framework of control Lyapunov R-functions. A novel composition rule allows the design of a composite control Lyapunov function with external level set that exactly shapes the maximal controlled invariant set and inner sublevel sets arbitrarily close to any choice of smooth ones, generalizing both pol...
متن کاملA new switching strategy for exponential stabilization of uncertain discrete-time switched linear systems in guaranteed cost control problem
Uncertain switched linear systems are known as an important class of control systems. Performance of these systems is affected by uncertainties and its stabilization is a main concern of recent studies. Existing work on stabilization of these systems only provides asymptotical stabilization via designing switching strategy and state-feedback controller. In this paper, a new switching strate...
متن کاملRobust Model Predictive Control of Constrained Supply Networks Via Invariant Ellipsoids Technique
The problem of robust control strategy synthesis for distributed supply network under demand uncertainty, time delays and state and control constraints is considered. An invariant ellipsoids approach is used for robust control problem solving, since the uncertain demands are regarded as an external disturbance. On the base Model Predictive Control approach, the designed control law implements i...
متن کاملSingular constrained linear systems
In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...
متن کاملLocal stabilization for a class of nonlinear impulsive switched system with non-vanishing uncertainties under a norm-bounded control input
Stability and stabilization of impulsive switched system have been considered in recent decades, but there are some issues that are not yet fully addressed such as actuator saturation. This paper deals with expo-nential stabilization for a class of nonlinear impulsive switched systems with different types of non-vanishing uncertainties under the norm-bounded control input. Due to the constraine...
متن کامل