Simple and Weak ∆-invariant Polyhedral Sets for Discrete-time Singular Systems
نویسندگان
چکیده
In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of ∆-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak ∆invariance are considered. They can be seen as extensions of the ∆-positive invariance concept used for the regular linear systems with additive disturbances. The results are presented by considering classical equivalent system representations for linear singular systems.
منابع مشابه
Generating Discrete Trace Transition System of a Polyhe-dral Invariant Hybrid Automaton
Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode trans...
متن کاملAdmissibility analysis for discrete-time singular systems with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model
This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...
متن کاملControlled Invariant Polyhedral Sets for Constrained Discrete-Time Descriptor Systems
This paper addresses the problem of constructing controlled invariant polyhedral sets for linear discrete-time descriptor systems subject to state and control constraints and persistent disturbances. Regardless the large number of contributions on set invariance for linear systems in the standard form, there are few works dealing with set invariance properties in the case of descriptor systems....
متن کاملInvariant approximations of robustly positively invariant sets for constrained linear discrete-time systems subject to bounded disturbances
This paper provides results on invariant approximations of robustly positively invariant sets for a discrete-time, linear, time-invariant system subject to state constraints. Two important sets, the minimal and the maximal robustly positively invariant sets and their approximations are investigated. Novel procedures for the computation of invariant approximations to these sets are presented. It...
متن کاملConstrained Robust Model Predictive Control Based on Polyhedral Invariant Sets by Off-line Optimization
This paper proposes a fast robust model predictive control using polyhedral invariant sets for uncertain polytopic discrete-time systems. A sequence of nested polyhedral invariant sets corresponding to a sequence of state feedback gains is constructed off-line. Thus, most of the computational burdens are moved off-line. At each sampling time, when the measured state lies between two adjacent po...
متن کامل