Matrix inequalities in the stability theory: new results based on the convolution theorem. (English. Russian original) Zbl 1521.93089
Autom. Remote Control 84, No. 3, 240-252 (2023); translation from Avtom. Telemekh. 2023, No. 2, 103-121 (2023).
Summary: Using Pyatnitskiy’s convolution theorem, the circle criterion of absolute stability for Lurie systems with several nonlinearities is obtained without use of the \(S\)-lemma. For connected systems with switching between three linear subsystems, a new criterion for the existence of a quadratic Lyapunov function is proposed. On the basis of the convolution theorem, two theorems are proved which lead to a substantial reduction in the dimensionality of connected systems of linear matrix inequalities. Issues of improving the circle criterion for Lurie systems with two nonlinearities are also discussed.
MSC:
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93D30 | Lyapunov and storage functions |
| 93C10 | Nonlinear systems in control theory |
| 93C05 | Linear systems in control theory |
Keywords:
switched systems; Lurie systems; stability; Lyapunov functions; matrix inequalities; circle criterionReferences:
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