M.S. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr., 43:475--482, 1998. Home/Search Document Details and Download
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Design of Observers for Hybrid Systems - Balluchi, Benvenuti, Di.. (2002) (5 citations) (Correct)
....the design parameter used to set the velocity of convergence in each location. As pointed out in [2] the stabilization of this continuous observer is more complex than the stabilization of a single dynamics in (10) and can be achieved using the results on hybrid systems stabilization presented in [5] and [16] In particular, exponential convergence of the hybrid observer is guaranteed by the following lemma: Lemma 1. Assume that HI: for i 1: N, all couples (Ai, Ci) in (5 5) are observable; H2: the hybrid system Hp exhibits transitions with time separation greater than or equal to ....
M. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. on Aut. Contr., 43(4):475-482, 1998.
Anytime Control Algorithm: Model Reduction Approach - Bhattacharya, Balas (2002) (Correct)
....us assume that z decays as z = A zz z . Therefore, the closed loop system while z is decaying is given by, 0 A 22 5 8 = 19) Thus we have three stable systems f 0 ; f 1 ; f 2 and a switching sequence that switches between them. We use multiple Lyapunov function approach[27] to prove stability of this switched linear system. The switching sequence S for this switched linear system is S = x 0 ; f 0 ; T 0 ) f 1 ; T 1 ) f 2 ; T 2 ) f 0 ; T 3 ) 20) which means that this hybrid system starts at time T 0 , with initial condition x 0 = fv 0 z 0 g and ....
....I(i) 2 f[T i ; T i 1 ) T i 3 ; T i 4 ) T i 3j ; T i 3j 1 ) g (21) where j 2 Z , Z is the set of non negative integers. De ne E(i) as the set of times when system f i is switched to, i.e. E(i) fT i ; T i 3 ; T i 3j ; g; j 2 Z (22) De nition (2. 2 in [27]) Given a strictly increasing sequence of times T = ft k g; k 2 Z , we say that V i (x ) is a Lyapunov like function for system f i and trajectory x = fv over T if: 1. V i is a positive de nite, continuous function about the origin (zero) 2. V i (x ) V i (x ) 8t 2 ....
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M. S. Branicky. Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems. IEEE Transactions in Automatic Control, 43(4):475-482, 1998.
Transformation of Linear Control Algorithms into Operationally .. - Bhattacharya (2003) (Correct)
....let us assume that z decays as z = A zz z . Therefore, the closed loop system while z is decaying is given by, 0 A 22 #( 2.17) Thus we have three stable systems f 0 , f 1 , f 2 and a switching sequence that switches between them. We use multiple Lyapunov function approach[Bra98] to prove stability of this switched linear system. The switching sequence S for this switched linear system is S = x 0 , f 0 , T 0 ) f 1 , T 1 ) f 2 , T 2 ) f 0 , T 3 ) 2.18) which means that this hybrid system starts at time T 0 , with initial condition x 0 = 32 0 z 0 and ....
....given by I(i) # [T i , T i 1 ) T i 3 , T i 4 ) T i 3j , T i 3j 1 ) 2.19) where j Z # , Z # is the set of non negative integers. Define as the set of times when system f i is switched to, i.e. i , T i 3 , T i 3j , # (2.20) Definition (2. 2 in [Bra98] Given a strictly increasing sequence of times t Z # , we say that V i (x ) is a Lyapunov like function for system f i and trajectory x over if: 1. V i is a positive definite, continuous function about the origin (zero) 2. V i (x ) #t # I(i) 3. V i is ....
[Article contains additional citation context not shown here]
M. S. Branicky. Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems. IEEE Transactions in Automatic Control, 43(4):475--482, 1998.
Implementation of Control Algorithms in an Environment of.. - Bhattacharya, Balas (Correct)
....and eqn. 6) are = 6 0 I 7 5 8 = 10) 6 0 A 22 7 5 8 = 11) Thus we have three stable systems f 0 ; f 1 ; f 2 and a switching sequence that switches between them. We use multiple Lyapunov function approach[6] to prove stability of this switched linear system. The switching sequence S for this switched linear system is S = x 0 ; f 0 ; T 0 ) f 1 ; T 1 ) f 2 ; T 2 ) f 0 ; T 3 ) 12) which means that this hybrid system starts at time T 0 , with initial condition x 0 = fv 0 z 0 g and ....
....given by I(i) 2 f[T i ; T i 1 ) T i 3 ; T i 4 ) T i 3j ; T i 3j 1 ) g ; j 2 Z (13) is the set of non negative integers. De ne E(i) as the set of times when system f i is switched to, i.e. E(i) fT i ; T i 3 ; T i 3j ; g; j 2 Z (14) De nition (2. 2 in [6]) Given a strictly increasing sequence of times T = ft k g; k 2 Z , we say that ) is a Lyapunov like function for system f i and trajectory x = fv g over T if: 1. V i is a positive de nite, continuous function about the origin (zero) 2. V i (x ) V i (x ) 8t 2 I(i) ....
[Article contains additional citation context not shown here]
M. S. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions in Automatic Control, 43(4):475-482, 1998.
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M.S. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr., 43:475--482, 1998.
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M.S. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automatic Control, 43(43):475--482, 1998.
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M. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr., 43:475--482, 1998.
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Branicky, M. S. Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems. IEEE Transactions on Automatic Control 43, 4 (1998), 475--482. Special issue on Hybrid Systems.
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M. S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Control, 43(4):475--482, 1998.
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M.S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automatic Control, 43(4):475--482, April 1998.
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M. S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Control, 43:475--482, 1998.
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M. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Contr., 43:475--482, 1998.
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M. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. on Automatic Control, 43(4):475--482, 1998.
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M. S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Automat. Control, 43:475--482, 1998.
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M. S. Branicky. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 43(4):475--482, 1998.
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