References
- Aubin , J , Lygeros , J , Quincampoix , M , Sastry , S and Seube , N . 2002 . Impulse Differential Inclusions: A Viability Approach to Hybrid Systems . IEEE Transactions on Automatic Control , 47 : 2 – 20 .
- Barles , G . 1985 . Deterministic Impulse Control Problems . SIAM Journal on Control and Optimization , 23 : 419 – 432 .
- Bensoussan , A and Lions , J . 1984 . Impulse Control and Quasi-variational Inequalities , England : Trans-Inter-Scientia .
- Branicky , M . 1997 . “ Stability of Hybrid Systems: State of the Art ” . In in Proceedings of the 36th IEEE Conference on Decision and Control , Vol. 1 , 120 – 125 . San Diego, California, USA : IEEE .
- Chen , M , Zhu , C and Feng , G . 2004 . Linear-matrix-inequality-based Approach to H ∞ Controller Synthesis of Uncertain Continuous-time Piecewise Linear Systems . IEE Proceedings-Control Theory and Applications , 151 : 295 – 301 .
- Cui , B , Han , M and Yang , H . 2005 . Some Sufficient Conditions for Oscillation of Impulsive Delay Hyperbolic Systems with Robin Boundary Conditions . Journal of Computational and Applied Mathematics , 180 : 365 – 375 .
- Feng , G . 2002 . Stability Analysis of Piecewise Discrete-time Linear Systems . IEEE Transactions on Automatic Control , 47 : 1108 – 1112 .
- Feng , G . 2005 . Robust Filtering Design of Piecewise Discrete Time Linear Systems . IEEE Transactions on Signal Processing , 53 : 599 – 605 .
- Filippov , A . 1988 . Differential Equations with Discontinuous Right-hand Side , The Netherlands : Kluwer Academic Publishers .
- Gaiko , V and Van Horssen , W . 2009 . A Piecewise Linear Dynamical System with Two Dropping Sections . International Journal of Bifurcation and Chaos , 19 : 1367 – 1372 .
- Guan , Z , Hill , D and Shen , X . 2005 . On Hybrid Impulsive and Switching Systems and Application to Nonlinear Control . IEEE Transactions on Automatic Control , 50 : 1058 – 1062 .
- Guan , Z and Lam , J . 2001 . Robust Stability of Composite Singular and Impulsive Interval Uncertain Dynamic Systems with Time Delay . International Journal of Systems Science , 32 : 1297 – 1307 .
- Huang , L . 1984 . Linear Algebra in Systems and Control Theory , China : Science Press .
- Johansson , M . 2002 . Piecewise Linear Control Systems: A Computational Approach , Germany : Springer .
- Johansson , M and Rantzer , A . 1998 . Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems . IEEE Transactions on Automatic Control , 43 : 555 – 559 .
- Li , X . 2010 . New Results on Global Exponential Stabilization of Impulsive Functional Differential Equations with Infinite Delays or Finite Delays . Nonlinear Analysis: Real World Applications , 11 : 4194 – 4201 .
- Liberzon , D and Morse , A . 1999 . Basic Problems in Stability and Design of Switched Systems . IEEE Control Systems Magazine , 19 : 59 – 70 .
- Liu , B and Liu , X . 2008 . Uniform Stability of Discrete Impulsive Systems . International Journal of Systems Science , 39 : 181 – 192 .
- Liu , Y and Zhao , S . 2009 . A New Approach to Practical Stability of Impulsive Functional Differential Equations in Terms of Two Measures . Journal of Computational and Applied Mathematics , 223 : 449 – 458 .
- Melin , J and Hultgren , A . 2006 . On Conditions for Regularity of Solutions for a Piecewise Linear System . Nonlinear analysis , 65 : 2277 – 2301 .
- Pan , S , Sun , J and Zhao , S . 2010 . Robust Filtering for Discrete Time Piecewise Impulsive Systems . Signal Processing , 90 : 324 – 330 .
- Pang , S , Deng , F and Mao , X . 2008 . Almost Sure and Moment Exponential Stability of Euler-Maruyama Discretizations for Hybrid Stochastic Differential Equations . Journal of Computational and Applied Mathematics , 213 : 127 – 141 .
- Rubensson , M and Lennartson , B . 2000 . Stability of Limit Cycles in Hybrid Systems using Discrete-time Lyapunov Techniques . Proceedings of the 39th IEEE Conference on Decision and Control . 2000 . Vol. 2 , pp. 1397 – 1402 . IEEE .
- Soh , C . 1999 . Robust Stability of Perturbed Periodic Hybrid Systems . International Journal of Systems Science , 30 : 811 – 821 .
- Tigan , G and Astolfi , A . 2007 . A Note on a Piecewise-linear Duffing-type System . International Journal of Bifurcation and Chaos , 17 : 4425 – 4429 .
- Wu , L , Ho , D and Lam , J . 2009 . H ∞ Model Reduction for Continuous-time Switched Stochastic Hybrid Systems . International Journal of Systems Science , 40 : 1241 – 1251 .
- Xu , H and Teo , K . 2009 . Stabilizability of Discrete Chaotic Systems via Unified Impulsive Control . Physics Letters A , 374 : 235 – 240 .
- Yang , T . 2001 . Impulsive Systems and Control: Theory and Applications , New York, USA : Nova Science .
- Yu , J , Zhang , K , Fei , S and Jiang , H . 2010 . Robust Fuzzy Control of Nonlinear Stochastic Delay Systems with Impulsive Effects . International Journal of Systems Science , 41 : 1163 – 1172 .
- Zhang , J , Johansson , K , Lygeros , J and Sastry , S . 2001 . Zeno Hybrid Systems . International Journal of Robust and Nonlinear Control , 11 : 435 – 451 .
- Zhang , Y and Sun , J . 2008 . Stability of Impulsive Functional Differential Equations . Nonlinear Analysis: Theory, Methods and Applications , 68 : 3665 – 3678 .
- Zhang , Y , Sun , J and Feng , G . 2009 . Impulsive Control of Discrete Systems with Time Delay . IEEE Transactions on Automatic Control , 54 : 830 – 834 .
- Zhao , S and Sun , J . 2010 . Controllability and Observability for Time-varying Switched Impulsive Controlled Systems . International Journal of Robust and Nonlinear Control , 20 : 1313 – 1325 .