Parameterized Robust Control Invariant Sets for Linear Systems: Theoretical Advances and Computational Remarks

• Published in: IEEE transactions on automatic control Vol. 55; no. 7; pp. 1599 - 1614
• Main Authors: Rakovic, Saša V, Baric, Miroslav
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Computation; Computer science; control theory; systems; Constraint optimization; Control Lyapunov functions; Control system synthesis; Control systems; Control theory. Systems; Discrete time systems; Disturbances; Exact sciences and technology; Invariants; linear polytopic case; Linear systems; Lyapunov functions; Lyapunov method; Modelling and identification; Optimization; Optimization methods; Robust control; Robust stability; Robust control; Polytope; Linear time invariant system; Control Lyapunov functions; Discrete time; Invariant set; linear polytopic case; Convex programming; Lyapunov function
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2010.2042341

We characterize a family of parametrized robust control invariant sets for linear discrete time systems subject to additive but bounded state disturbances. The existence of a member of the introduced family of parametrized robust control invariant sets can be verified by solving a tractable convex optimization problem in the linear convex case, which reduces to the standard linear or convex quadratic programme in the linear polytopic case. The developed method can also be utilized to detect and obtain an implicit representation of local control Lyapunov functions in the linear convex case from the solution of a single and tractable convex optimization problem. The offered method permits for the computation of polytopic robust control invariant sets and local control Lyapunov functions of indirectly controlled and limited complexity in the linear polytopic case.