Amato, F.; De Tommasi, G.; Pironti, A. Input-output finite-time stabilization of impulsive linear systems: necessary and sufficient conditions. (English) Zbl 1329.93122 Nonlinear Anal., Hybrid Syst. 19, 93-106 (2016). Summary: The main result of this paper consists of a pair of necessary and sufficient conditions for the input-output finite-time stability of impulsive linear systems. The former requires that an optimization problem, constrained by a coupled differential/difference Linear Matrix Inequality (LMI), admits a feasible solution; the latter that the solution of a coupled differential/difference Lyapunov equation satisfies a constraint on the maximum eigenvalue. The first condition was already provided in F. Amato, G. Carannante, G. De Tommasi [”Input-output finite-time stabilisation of a class of hybrid systems via static output feedback”, Int. J. Control 84, No. 6, 1055-1066 (2011; Zbl 1245.93119)], where, however, only sufficiency was proven. The novel analysis condition (i.e. the one requiring the solution of the differential/difference Lyapunov equation) is shown to be more efficient from the computational point of view, while the result based on the differential/difference LMI is the starting point for the derivation of the design theorem. Some examples illustrate the benefits of the proposed technique. Cited in 17 Documents MSC: 93D25 Input-output approaches in control theory 93C05 Linear systems in control theory 34A37 Ordinary differential equations with impulses 93B60 Eigenvalue problems Keywords:impulsive dynamical linear systems; IO-FTS; D/DLMIs; D/DLE Citations:Zbl 1245.93119 Software:LMI toolbox; SeDuMi Interface PDFBibTeX XMLCite \textit{F. Amato} et al., Nonlinear Anal., Hybrid Syst. 19, 93--106 (2016; Zbl 1329.93122) Full Text: DOI References: [1] Zhang, J.; Makris, N., Rocking response of free-standing blocks under cycloidal pulses, J. Eng. Mech., 127, 5, 473-483 (2001) [2] Pettersson, S., Analysis and design of hybrid systems (1999), Chalmers University of Technology, (Ph.D. dissertation) [3] Amato, F.; Ambrosino, R.; Cosentino, C.; De Tommasi, G., Input-output finite-time stabilization of linear systems, Automatica, 46, 9, 1558-1562 (2010) · Zbl 1202.93142 [5] Amato, F.; Carannante, G.; De Tommasi, G., Input-output finite-time stabilisation of a class of hybrid systems via static output feedback, Internat. J. Control, 84, 6, 1055-1066 (2011) · Zbl 1245.93119 [6] Huang, S.; Xiang, Z.; Karimi, H., Input-output finite-time stability of discrete-time impulsive switched linear systems with state delays, Circuits Systems Signal Process., 33, 1, 141-158 (2014) [7] Ma, H.; Jia, Y., Input-output finite-time mean square stabilisation of stochastic systems with Markovian jump, Internat. J. Systems Sci., 45, 3, 325-336 (2014) · Zbl 1307.93443 [8] Amato, F.; Ambrosino, R.; Cosentino, C.; De Tommasi, G., Finite-time stabilization of impulsive dynamical linear systems, Nonlinear Anal. Hybrid Syst., 5, 1, 89-101 (2010) · Zbl 1371.93159 [9] Liberzon, D., Switching in Systems and Control (2003), Birkhäuser · Zbl 1036.93001 [10] Amato, F.; Carannante, G.; De Tommasi, G.; Pironti, A., Input-output finite-time stability of linear systems: necessary and sufficient conditions, IEEE Trans. Automat. Control, 57, 12, 3051-3063 (2012) · Zbl 1369.93556 [11] Medina, E., Linear impulsive control systems: A geometric approach (2007), School of Electrical Engineering and Computer Science, Ohio University, (Ph.D. dissertation) [12] Medina, E.; Lawrence, D., State feedback stabilization of linear impulsive systems, Automatica, 45, 6, 1476-1480 (2009) · Zbl 1166.93362 [13] Amato, F., Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters (2006), Springer Verlag · Zbl 1142.93001 [14] Becker, G.; Packard, A., Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback, Systems Control Lett., 23, 205-215 (1994) · Zbl 0815.93034 [15] Amato, F., (Finite-Time Stability and Control. Finite-Time Stability and Control, Lectures Notes in Control and Information Sciences, vol. 453 (2014), Springer) · Zbl 1297.93001 [17] Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M., LMI Control Toolbox (1995), The Mathworks Inc. [18] Briat, C., Convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled-data systems under dwell-time constraints, Automatica, 49, 11, 3449-3457 (2013) · Zbl 1315.93058 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.