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- Pettersson, Stefan, 1969, et al.
(författare)
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Controller Design of Hybrid Systems
- 1997
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Ingår i: Hybrid and Real-Time Systems, HART'97, Lecture Notes in Computer Science 1201, Editor O. Maler, Springer. ; , s. 240-54
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present two strategies to design a hybrid controller for a system described by several nonlinear vector fields. Besides the overall goal to find a controller that stabilizes the closed-loop hybrid system, the selection will also be made in such a way that an exponentially stable closed-loop system is obtained. The design strategies are based on stated stability and exponential stability theorems for hybrid systems. The first approach results in regions where it is possible to change vector fields guaranteeing (exponential) stability of the closed-loop hybrid system. The second design strategy utilizes the fact that a system is (exponentially) stable if it is always possible to choose a vector field that points in a direction such that the trajectory approaches the equilibrium point. These conditions can be verified by solving a linear matrix inequality (LMI) problem.
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- Pettersson, Stefan, 1969, et al.
(författare)
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Exponential Stability Analysis of Nonlinear Systems using LMIs
- 1997
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Ingår i: Proc. of 36th IEEE Conference on Decision and Control, San Diego, DEC 10-12. ; , s. 199-204
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Konferensbidrag (refereegranskat)abstract
- This paper presents a constructive method for showing exponential stability of autonomous nonlinear systems consisting of state-dependent weighted linear systems. This kind of system representation is common in for instance fuzzy systems or is the result of an exact or approximative description of an arbitrary nonlinear vector field. Stability is shown by joining multiple local Lyapunov functions properly in the state-space. The overall Lyapunov function, consisting of the local ones, are allowed to be discontinuous at the states where the trajectory passes from one local region to another. By using local quadratic Lyapunov functions the stability conditions are formulated as linear matrix inequalities (LMIs), which can be solved efficiently by computerized methods.
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- Pettersson, Stefan, 1969, et al.
(författare)
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LMI for Stability and Robustness of Hybrid Systems
- 1997
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Ingår i: Proc. 1997 American Control Conference, Albuquerque, New Mexico,JUN 04-06. ; , s. 1714-18
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Konferensbidrag (refereegranskat)abstract
- This paper presents results for stability and robustness of hybrid systems consisting of nonlinear subsystems. Present stability results that are extensions of classical Lyapunov theory are restricted to certain kinds of hybrid systems. For example, it is required that all subsystems have the same equilibrium point. In this paper these results are generalized, but more importantly, it is shown how Lyapunov functions for hybrid systems can be solved by linear matrix inequalities (LMI). Furthermore, it is shown how uncertainties around the nominal switch sets can be handled by introducing acceptable switch regions as additional stability conditions. The theory is illustrated by an example.
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