已知某离散系统的差分方程为[tex=13.071x1.357]Lt3u4RzqJIdx+izJhOoNIEGar5YJhPW49hUBGh7C0cw=[/tex], 激励为 [tex=6.0x1.5]oydPfO5ICrEiCwwuDMxdOaTgY1To0sc66U2/A7R7jKg=[/tex],初始状态[tex=7.929x1.357]0P7qpPwM+qakoydyJcPsPSZq8+1MWG6/1N9JjaumEMs=[/tex], 试求该系统的零输入响应，零状态响应和全响应。
解 将差分方程移序变换得[p=align:center][tex=18.786x4.643]UD5Uh4Sf0JOreHxD3gt15t2A7AD2xPM4rYCUnX5XFGP9uzdl1dOBmorwFcBiAL46IFzP3k2b3cMbCTUPHkXRYTQ+txpV26j0asxql0GuETiEyfvWr34Y6x0xQd4vgFL9kZ3/y9WbxLQVa9ziixhoBmnK5YACUTr20kWpeyJSg2QgCxkHOSit+90cWUph67Ns89RBnytcOSsraJRfrj342Q==[/tex]移序转移算子[tex=8.071x2.571]ni5D6+vf/yxEqm1uTtiRjqQhjeBITnt62boIB6mkalz/GeP33/70xKtXwe+fTqRL[/tex], 解得特征方程 [tex=5.786x1.357]hQK4Ej0/1+GrWhaLwbGQaw==[/tex], 特征根 [tex=5.357x1.214]HLfKl2WtZa0QWV/LGX78xCfxK9v4omFijGlI3Z0H4Ks=[/tex], 将移序算子分解成[p=align:center][tex=14.786x2.714]3K5HP6aByfI8qJvDaTcJ6BRBe9lyLKTPF5pAEvbIpHMsozZATnsnuAIgY13Lk6XXqsX4pcE/7Cdc2oD8RVVEznbm4Tl00Ao4jP6iTOA0tR21cwaHO91/0uQTYk3c1oBZ[/tex]则单位函数响应 [tex=13.286x2.786]WwB1gNv+UXoM1W41cg+lhYaei6y1YvQaTjIanSCLmiIIpMcprjSbvKtg8qd0roL/yhZP4o/2CTFkBtbVBvwt6EX4YlcHJdEnOi1hdf3AoSnHO3oDOSp5nZ6BaZbXKozd[/tex]零输入响应 [tex=12.786x1.571]9Ixh85+w2mQgYCy22rTlrI3Q7uyOMt2w3eE+vJ6e7cRRhpOOMohOtt5ZqU9+TSWQ9R/f0DhBxKPlq3vVGvpzNdgkmeKJwH8zVYuUhaL+n/s=[/tex]由初始状态可得[p=align:center][tex=24.5x3.071]qeiYnKXLEhyhuGRg8yLtr44q9bfPmvPhjYnsSdfWxcY/cDjG8TI9Iv2G3wwFgw2fhcIuylvDe6Zn040PYYNq5tmIaV3DAdHYoyruy+u0leQLY+NIVYUWb1fe1QTUMOwJFyUPyjiPTbKWFCztg4GOJj/MfJJVuUwDatRIe5G2KtiJBnpQ3qTWzLluBVPPx7pL12IbnEgu+aTK096kx+dUOw==[/tex]由此得[p=align:center][tex=21.0x1.357]PQ4Yr0oCfLUkBwEt6lKmdjP8ZpY13ieVKpuu4oQUegE2b1oIjD8w3fsbXNJuDzvF8iEJzshbv8j5mAnTL9j8jjYD8CkZVlnX3hGovFyI2hI=[/tex]从而[p=align:center][tex=6.429x2.357]aWDmgTKGMwAZkdJZ+0/q3LPvJ6iJFOyaujFBLZ8jD5iZyEAk6AflrHKG8ZvgG9fbQTSV9XkftQVkkBR0PMcD7w==[/tex]则[p=align:center][tex=12.786x2.357]nagmXiL2ImqZMchVFiQuL73n6Ydf2PC2MyC9JzGzpALhiPkzadku1mDaa74aMqvf/FVTchjzcssC06d0kOOxRiKQ3wvjwd3EaYVhIYEyhy8=[/tex]零状态响应[p=align:center][tex=27.714x9.286]4vfCoH8bUZkSkWrSR6VhTnJfsLF3MC2tm92TN7LL/nrCPtiAvPkrl4hLtynzVPCpag5qbxqBOTdTXdxEC0OgUGNB85Re7xEaC/Z5ZsrD/5CD4U8Py55c80TfirIG5OrINSDQ8Vh1oTq+bVzewMRbHp0hs2Bh+b6yTVy9uCVcwUd3cStBeVB4YGjVxSIrGMcQEOHqQVB2nj3mL9fYLQUu4/j52+ffx3u3ayjNlHXQ14Xzqgt3nO6PGQ7nD77WeSNCtR0k0WiMhPzAHFyKu/hehStN9Hvlman82yt18IK0mXYWzoQ1/DRSquphf+tlQMH9bqWyd9W79yhp1AnY0GLTMemgvFd85rLIeBUI7IbM4D3jOusAFGRlwJDVGhvvK4PlhtGyMyEiFNB7vqsHXM2uJA12wKM3QIZJe7Urq/3XIw92h1SLkc8zC0gYYqFnwCwpkodpsnjaqZrhkD/5nwZmKJIJ2UM7WYMtwJDAtXP7oMp7rL31awviEtuKl7imUN/3sInKMz4SZBMGGeKSI35WCWgXxjIc0PmkGuRNjhvdvx0uunqNjDZeac0tvEHaGnYdv1kHvRuVI3HWwC7a81GHOQ==[/tex]则 [tex=20.214x2.786]JtZwFrQ+JAcAetwaWXXAhTSDp3pTh9F7M7pHz3weLCb4w2w6TQipiWDvjHx8he8QVs9BCCOMDQBUbBfXPmuPbDZTod5NS3hbpjGqNkIGvlAPOyC8cC7IfsvLjaCEa5I+3iIN9rs0PsVrHLVwU4ZKZ4cBhGaEu9imymRK4t0rvfQ=[/tex]全响应 [tex=25.786x2.786]N9ySoaQdvIpxMPOD8w1lo8gVB7zZ5sEvOLH8AF2qfoDekjhc5qXeX2psI0j1zHqr0wXur46WUDMea9/8OKrKIPzV8MbnfgI440oIvBQXkubWfMo+MHXqxkVawo0EM65kZq1dsxMVcxgNFi6MKLEVpGfSC+p541Atx+bUTThMk5qjecjjZPCyihCwjdPwzJt+[/tex]
举一反三
- 求下列差分方程所描述的离散系统的零输入响应,零状态响应和全响应。[tex=19.071x1.357]zVtlD8wh3ZsJinYEiFPSrYwjUZ7xZeznNDrVSuJmROhzc3BkHp3P261cvCwaMSa7wpaunPBjOAt3+NTvesi3mw==[/tex]
- 求下列差分方程所描述的离散系统的零输入响应,零状态响应和全响应。[tex=21.643x1.357]ud+ivWDQhaADNFKIjM6tRqq0RY2q2Uc3gIv8287wMfsaKuSxiz11F42TD4ublcaahNJZlP79mpRKAubC3jBc0w==[/tex]
- 求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应、零状态响应和全响应。[br][/br][tex=19.357x1.357]wffO7E8wJIKHv8gtbaTS87POBWf3XlQx44H1IOFMBLS2Uw5OL4DpOI55zKhlrdAK[/tex]
- 求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应、零状态响应和全响应。[br][/br][tex=19.071x1.357]m42gBaifKux86I+xVF46Xej5ZiUA9t6Vb7HI3Wn+xu6mZRXQXnc4sAVqRKOe+EZG[/tex]
- 求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应、零状态响应和全响应。[br][/br][tex=22.071x1.357]m42gBaifKux86I+xVF46XctbWZVNtUHFgXCMbgQ1TPMHGxtPFRX1eSe7kAUrpZFJ[/tex]
内容
- 0
求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应、零状态响应和全响应。[br][/br][tex=26.643x1.357]+Gt8zI6whkNVgNF8fkINp8huRvtjsEbCuhQ8pwXq6K3JzPJEtiePsN3yaYHftEkFlX39fawUXF9OCpvrSxDpXw==[/tex]
- 1
求下列差分方程所描述的离散系统的零输入响应,零状态响应和全响应。[tex=18.643x1.5]ud+ivWDQhaADNFKIjM6tRullnsggWxOJcxZzFqZD/NmYeTLPRyBipMpCupHUrIdd9ZEzTvrTQq0Bcf8wcRO2dg==[/tex]
- 2
若描述系统的差分方程为 [tex=22.929x1.357]CoDTT0hXm9Xd1OZzCJ6dmDAOXus+eF4skwiNv9QFEBCy/9qI+W8bBaZ0I3IkQgc/[/tex], 已知 [tex=12.429x1.357]FBOluitloG3rOOLj/Ek1IBt2sPAlSGutcycxELRKEys=[/tex], 求系统的零输入响应和零状态响应。
- 3
求下列差分方程所描述的[tex=1.714x1.0]ptAt65AfwA4koryK6UNdFg==[/tex]离散系统的零输入响应、零状态响应和全响应。[br][/br][tex=19.643x1.357]gVzaoqtwrme/yxT2qYwg7XoIuXQTskYR/d6k6A0QZrnBfW/OysIYnEBeH18P6YQH[/tex]
- 4
求下列差分方程所描述的离散系统的零输入响应、零状态响应和完全响应。[tex=16.929x2.786]Gyx6TpdDSt3yDRLJF7ntELlOOlZhotAJXwnmEBNCzosFbw0sGRBYl6jaQmEx9XQD3Ec8ruzKIea4aDp64txoN2Q/PO9wJCSXdX3v98ezudo=[/tex]